Charles P. Boyer and
Krzysztof Galicki. Sasakian Geometry, Oxford University Press, Oxford link
and Amazon link This work was partially supported by several NSF Grants.
I am maintaining an erratum for our book, which will be periodically updated. Hopefully it will have an end! The erratum for `Sasakian Geometry' in the form of a pdf file
is here.
E-Preprints:
Charles P. Boyer, Hongnian Huang, Eveline Legendre, and Christina T{\o}nnesen-Friedman, Existence and Non-Existence of Constant Scalar Curvature and Extremal Sasaki Metrics, pdf file posted October 25, 2022. This work was partially supported by grant #519432 from the Simons Foundation.
Charles P. Boyer, and Christina T{\o}nnesen-Friedman, Constant Scalar Curvature Sasaki Metrics and Projective Bundles, pdf file posted Dec. 2, 2021, to appear in Birational Geometry,
Kähler-Einstein Metrics, and Degeneration in the Springer Proceedings in
Mathematics & Statistics, (2023).
This work was partially supported by grant #519432 from the Simons Foundation.
Charles P. Boyer, and Christina T{\o}nnesen-Friedman, The $S^3_\bfw$ Sasaki Join Construction, pdf file posted November 26, 2019, in final form September 28, 2021. Published in J. Math. Soc. Japan 74, No. 4 (2022), pg 1335-1371 ("https://doi.org/10.2969/jmsj/83828382"). This work was partially supported by grant #519432 from the Simons Foundation.
Charles P. Boyer, Hongnian Huang, Eveline Legendre, and Christina T{\o}nnesen-Friedman, Some Open Problems in Sasaki Geometry, pdf file posted July 20, 2019, published version in Differential Geometry in the Large , Dearricott, Tuschmann, Nikolayevsky,
Leistner, and Crowley, editors, London Mathematical Society Lecture Notes 463, Cambridge University Press, 2021. This work was partially supported by grant #519432 from the Simons Foundation.
Charles P. Boyer, and Christina T{\o}nnesen-Friedman, Sasaki-Einstein Metrics on a class of 7-Manifolds, pdf file posted November 20, 2018, Journal of Geometry and Physics 140 (2019) 111-124; journal link. This work was partially supported by grant #519432 from the Simons Foundation.
Charles P. Boyer, Contact Structures of Sasaki Type and their Associated Moduli,
pdf file, posted Oct. 17, 2018, Complex Manifolds 6 (1) (2019) 1-30; journal link. This work was partially supported by grant #519432 from the Simons Foundation.
Charles P. Boyer, and Christina T{\o}nnesen-Friedman, On Positivity in Sasaki Geometry, pdf file posted August 9, 2018, Geometriae Dedicata 204 (2020) 149-164. This work was partially supported by grants #245002 and #519432 from the Simons Foundation.
Charles P. Boyer, David M.J. Calderbank, and Christina T{\o}nnesen-Friedman, The K\"ahler geometry of Bott manifolds, pdf file posted January 29, 2018. Advances in Mathematics 350 (2019), 1-62;
journal link . This work was partially supported by grants #245002 and #519432 from the Simons Foundation.
Charles P. Boyer, Hongnian Huang, and Eveline Legendre, An application of the Duistermaat-Heckman Theorem and its extensions in Sasaki Geometry, pdf file posted Dec. 2, 2017, Geometry & Topology 22 (2018) 4205-4234; journal link . This work was partially supported by grants #245002 and #519432 from the Simons Foundation.
Charles P. Boyer, and Craig van Coevering, Relative K-stability and Extremal Sasaki metrics, posted August 19, 2016, and in revised form, pdf file December 20, 2016, Mathematical Research Letters, 25 (1) (2018), 1-19. journal link. This work was partially supported by grant #245002 from the Simons Foundation.
Charles P. Boyer, Hongnian Huang, Eveline Legendre, and Christina T{\o}nnesen-Friedman, Reducibility in Sasakian Geometry, pdf file posted June 16, 2016, and in revised form 2/10/18, Transactions of the American Mathematical Society 370 (10) (2018), 6825-6860. journal link. This work was partially supported by grant #245002 from the Simons Foundation.
Charles P. Boyer, Leonardo Macarini, and Otto van Koert, Brieskorn Manifolds, Positive Sasakian Geometry, and Contact Topology, pdf file posted June 29, 2015; Forum Mathematicum 28 (5) (2016), 943-965. Journal Link file 11/20/15). This work was partially supported by grant #245002 from the Simons Foundation.
Charles P. Boyer, Hongnian Huang, Eveline Legendre, and Christina T{\o}nnesen-Friedman, The Einstein-Hilbert functional and the Sasaki-Futaki invariant, pdf file posted June 26, 2015, and in revised form 9/23/15, International Mathematics Research Notices (2017) 2017 (7): 1942-1974. This work was partially supported by grant #245002 from the Simons Foundation.
Charles P. Boyer and Christina T{\o}nnesen-Friedman, The Sasaki Join and Admissible K\"ahler Constructions, pdf file posted June 2, 2015 Journal of Geometry and Physics 91 (2015) 29-39; journal link. This work was partially supported by grant #245002 from the Simons Foundation.
Charles P. Boyer and Christina T{\o}nnesen-Friedman, Simply Connected Manifolds with Infinitely Many Toric Contact Structures and Constant Scalar Curvature Sasaki Metrics, pdf file posted February 11, 2014. This unpublished work was partially supported by grant #245002 from the Simons Foundation.
Charles P. Boyer and Christina T{\o}nnesen-Friedman, The Sasaki Join, Hamiltonian 2-forms, and Constant Scalar Curvature, pdf file posted February 11, 2014, and in revised form on August 19, 2014. The final version of this work combines much of the analysis in the two papers arXiv:1402.2546 and arXiv:1309.7067v3 which appears in the Journal of Geometric Analysis 26 (2016) 1023-1060, pdf file posted January 16, 2015. Journal link. This work was partially supported by grant #245002 from the Simons Foundation.
Charles P. Boyer and Christina T{\o}nnesen-Friedman, The Sasaki Join, Hamiltonian 2-forms, and Sasaki-Einstein Metrics, pdf file posted October 1, 2013, in second revised form on June 19, 2014, the final version of this work has been significantly streamlined with a new title: On the Topology of some Sasaki-Einstein Manifolds pdf file posted January 16, 2015. It appears in the New York Journal of Mathematics 15 (2015) 57-72 journal link, This work was partially supported by grant #245002 from the Simons Foundation.
Charles P. Boyer and Christina T{\o}nnesen-Friedman, Extremal Sasakian Geometry on S^3-bundles over Riemann Surfaces, pdf file posted February 4, 2013 (International Mathematics Research Notices 2014, No. 20 (2014), 5510-5562); journal link. This work was partially supported by grant #245002 from the Simons Foundation.
Charles P. Boyer and Christina T{\o}nnesen-Friedman, Sasakian Manifolds with Perfect Fundamental Group, pdf file posted October 9, 2012, and in revised form November 15, 2012 (African Diaspora Journal of Mathematics, 14 (2012), no. 2, pp. 98-117; journal link. This work was partially supported by grant #245002 from the Simons
Foundation.
Charles P. Boyer and Justin Pati, On the Equivalence Problem for Toric Contact Structures on S^3-bundles over S^2,
pdf file(590K), posted April 11, 2012 (Pacific Journal of Mathematics 267 (2) (2014) 277-324), Journal Link. This work was partially supported by grant #245002 from the Simons Foundation.
Charles P. Boyer and Christina T{\o}nnesen-Friedman, Extremal Sasakian Geometry on T^2\times S^3 and Related Manifolds, pdf file posted August 10, 2011, revised version posted September 7, 2011, second revised version posted February 17, 2012, third revised version December 12, 2012 (Compositio Mathematica 149 (2013) 1431-1456), Journal Link. This work was partially supported by grant #245002 from the Simons Foundation.
Charles P. Boyer, Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S^2\times S^3, Symmetry, Integrability and Geometry: Methods and Applications, SIGMA 7 (2011), 058, 22 pages;
pdf file(322K), journal version June 15, 2011; original version posted January 28, 2011.
Charles P. Boyer, Maximal Tori in Contactomorphism Groups,
pdf file(408K) posted March 7, 2010, in revised form August 19, 2012, second revised form December 12, 2012, (Differential Geometry and Applications 31 (2013) 190-216), Journal Link. This work was partially supported by NSF Grant DMS-0504367.
Charles P. Boyer, Extremal Sasakian metrics on S^3-bundles over S^2,
pdf file(198K) posted February 4, 2010, and
in revised form January 28, 2011 (Math. Res. Lett. 18 (2011), no. 01, 181-189),
Journal Link.
This work was partially supported by NSF Grant DMS-0504367.
Charles P. Boyer,
The Sasakian Geometry of the Heisenberg Group,
pdf file(
240K)
posted April 8, 2009 (Bull. Math. Soc. Sci. Math. Roumanie 52 (3), 2009, 251-262),
Journal Link.
This work was partially supported by NSF Grant DMS-0504367.
Charles P. Boyer and Michael Nakamaye,
On Sasaki-Einstein Manifolds in Dimension Five,
pdf file(
340K)
posted March 1, 2009, and in revised form on April 30, 2009 (Geometriae Dedicata 144 (1) (2010) 141-156) Springer Link.
This work was partially supported by NSF Grant DMS-0504367.
Charles P. Boyer,
Sasakian Geometry: The Recent Work of Krzysztof Galicki (Note di Matematica,
vol. 28, suppl. n. 1 (2008), pp. 63-105). Journal Link,
Postscript file (573K)pdf file(340K)
posted June 2, 2008, and in revised form June 17, 2008.
This work was partially supported by NSF Grant DMS-0504367.
Charles P. Boyer,
Krzysztof Galicki, and Santiago Simanca.
The Sasaki Cone and Extremal Sasakian Metrics, Proceedings of the Conference on Riemannian Topology, pg 263-290, K. Galicki & S. Simanca, Eds, Birkhauser, Boston, 2008.
Postscript file (573K)pdf file(340K) posted
December 30, 2007. This work was partially supported by NSF Grant DMS-0504367.
Charles P. Boyer and
Krzysztof Galicki.
Sasakian Geometry, Holonomy, and Supersymmetry, (in Handbook of pseudo-Riemannian Geometry
and Supersymmetry)
Postscript file (677K)pdf file(403K) posted
March 9, 2007 (revised version posted September 13, 2007). This work
was partially supported by NSF Grant DMS-0504367.
Charles P. Boyer,
Krzysztof Galicki, and Santiago Simanca.
Canonical Sasakian Metrics (Communications in Mathematical Physics 279 (2008), 705-733) Springer link,
Postscript file (376K)pdf file(364K) posted
April 13, 2006, and in revised form March 8, 2007. This work was partially supported by NSF Grant DMS-0504367.
Charles P. Boyer,
Krzysztof Galicki, and Liviu Ornea.
Constructions in Sasakian Geometry. (Mathematische Zeitscrift 257 (2007), 907-924) Springer link,
Postscript file (313K)pdf file(314K) posted
February 11, 2006 (updated 1-22-07). This work
was partially supported by NSF Grants DMS-0203219 and DMS-0504367.
Charles P. Boyer and
Krzysztof Galicki.
Highly Connected Manifolds with Positive Ricci Curvature. (Geometry and Topology 10 (2006), 2219-2235) G&T link ,
Postscript file (230K)pdf file(294K) posted
August 12, 2005, and in revised form September 13, 2007. This work
was partially supported by NSF Grants DMS-0203219 and DMS-0504367.
Charles P. Boyer and
Krzysztof Galicki.
Sasakian Geometry and Einstein Metrics on Spheres, (Perspectives in Riemannian Geometry,
Proceedings on Short Program on Riemannian Geometry, CRM Montr\'eal, Canada, Vol 40 (2006),
47-61).
Postscript file (419K)pdf file(179K) posted
April 19, 2005. This work
was partially supported by NSF Grant DMS-0203219.
Charles P. Boyer,
Krzysztof Galicki, and Paola Matzeu.
On Eta-Einstein Sasakian Geometry, (Commun. Math. Phys 262 (2006), 177-208) Springer link,
Postscript file (381K)pdf file
(378K) posted June 30, 2004, and in latest revised form, Oct. 31, 2005.
This work
was partially supported by NSF Grant DMS-0203219.
Charles P. Boyer,
Krzysztof Galicki,
Sasakian Geometry, Hypersurface Singularities, and Einstein Metrics,
(Supplemento ai Rendiconti del Circolo Matematico di Palermo Serie II. Suppl 75 (2005), 57-87).
Postscript file (404K)pdf file
(452K) posted May 13, 2004.
This work
was partially supported by NSF Grant DMS-0203219.
Charles P. Boyer,
Krzysztof Galicki,
Einstein Metrics on Rational Homology Spheres (Journal of Differential Geometry 74 (2006), 353-362)
Postscript file (173K)pdf file
(207K) posted November 20, 2003.
This work
was partially supported by NSF Grant DMS-0203219.
Charles P. Boyer,
Krzysztof Galicki,
János
Kollár , and Evan Thomas .
Einstein Metrics on Exotic Spheres in Dimensions 7,11, and 15, (Experimental Mathematics 14 (2005), 61-66).
Postscript file (176K)pdf file
(215K) posted November 17, 2003.
This work
was partially supported by NSF Grant DMS-0203219.
Charles P. Boyer,
Krzysztof Galicki, and
János
Kollár .
Einstein Metrics on Spheres, (Annals of Mathematics 162(1) (2005), 557-580) Annals of Math link,
Postscript file (293K)pdf file
(308K) posted September 24, 2003,
and in revised form July 12, 2004. This work
was partially supported by NSF Grant DMS-0203219.
Charles P. Boyer,
Krzysztof Galicki.
New Einstein Metrics on $8\#(S^2\times S^3)$
( Diff. Geom.
and Its Applications 19 (2003), 245-251),
Postscript file (19K)pdf file
(20K) posted August 27, 2002.
This work
was partially supported by NSF Grants DMS-9970904 and DMS-0203219.
Charles P. Boyer,
Krzysztof Galicki.
Rational Homology 5-spheres with Positive Ricci Curvature, (Math. Res. Lett. 9 (2002), 521-528),
Postscript file (213K)pdf file
(231K) posted March 6, 2002. This work
was partially supported by NSF Grants DMS-9970904 and DMS-0203219.
Charles P. Boyer,
Krzysztof Galicki,
and Michael Nakamaye.
Sasakian Geometry, Homotopy Spheres and Positive Ricci Curvature, (Topology 42 (2003), 981-1002),
Postscript file (359K)pdf file
(375K) posted January 16, 2002, revised May 10, 2002. This work
was partially supported by NSF Grant DMS-9970904 and DMS-0203219.
Charles P. Boyer,
Krzysztof Galicki,
and Michael Nakamaye.
Einstein Metrics on Rational Homology 7-Spheres, (Ann. Inst. Fourier 52 (2002), 1569-1584),
Postscript file (331K)pdf file
(312K) posted August 19, 2001. This work
was partially supported by NSF Grant DMS-9970904 and DMS-0203219. A copy of just the table
of our list of Sasakian-Einstein rational homology 7-spheres is available as a
Postscript file, or pdf file.
Charles P. Boyer,
Krzysztof Galicki,
and Michael Nakamaye.
On Positive Sasakian Geometry
Postscript file (536K)pdf file
(1743K) posted April 19, 2001 (revised version posted February 22,2002).
( Geometriae Dedicata 101 (2003), 93-102.) This work
was partially supported by NSF Grant DMS-9970904.
Charles P. Boyer,
Krzysztof Galicki,
and Michael Nakamaye.
Sasakian-Einstein Structures on $9\#(S^2\times S^3)$ (Trans. Amer. Math. Soc. 354 (2002), 2983-2996.)
Postscript file (617K)pdf file
(2434K) posted February 22, 2001. This work
was partially supported by NSF Grant DMS-9970904.
Charles P. Boyer,
Krzysztof Galicki,
and Michael Nakamaye.
On the Geometry of Sasakian-Einstein 5-Manifolds
(Math. Ann. 325
(2003), 485-524.)
Postscript file (937K)pdf file
(5970K) revised version posted March 6, 2001,
This work
was partially supported by NSF Grant DMS-9970904.
This article uses a modification of a C code originally
written by Jennifer Johnson and János Kollár. The original codes can
be found at
Jennifer Johnson's web page.
To see our modified code click
here.
.
Charles P. Boyer,
Krzysztof Galicki,
and
Paolo Piccinni.
3-Sasakian Geometry, Nilpotent Orbits, and Exceptional Quotients,
(Annals of Global Analysis and Geometry 21 (2002), 85-110)
Postscript file (721K)pdf file
(4000K) posted July 30, 2000. This work
was partially supported by NSF Grant DMS-9970904.
Charles P. Boyer and
Krzysztof Galicki.
New Einstein Metrics in Dimension Five (J. Diff. Geom. 57 (2001), 443-463)
Postscript file (633K)pdf file
(2790K) posted March 24, 2000. This work
was partially supported by NSF Grant DMS-9970904.
Charles P. Boyer and
Krzysztof Galicki.
Einstein Manifolds and Contact Geometry
(Proc. of AMS. 129(8) 2001, 2419-2430.).
Postscript file (555K)pdf file
(2222K) posted December 2, 1999. This work
was partially supported by NSF Grant DMS-9970904.
Charles P. Boyer and
Krzysztof Galicki.
A Note on Toric Contact Geometry.
(J. of Geom. and Phys. 35 (2000) 288-298.).
Postscript file (56.9K)pdf file
(1852K) -posted July 8, 1999, in revised form Sept. 17, 1999. This work
was partially supported by NSF Grant DMS-9970904.
Charles P. Boyer and
Krzysztof Galicki.
On Sasakian-Einstein Geometry.
(Int. J. of Math. 11 (2000) 873-909.).
Postscript file (479K)pdf file
(6673K) -posted Nov. 18, 1998. This work
was partially supported by NSF Grants DMS-9423752 and DMS-9970904.
Charles P. Boyer and
Krzysztof Galicki.
3-Sasakian Manifolds.
(Essays on Einstein Manifolds, C. LeBrun and
M. Wang, Eds., Surveys in Differential Geometry, Vol. VI. Supplement to JDG. ).
Postscript file (876K)pdf file
(13685K) -posted Sept. 9, 1998 (revised version posted Oct. 30, 1998). This work
was partially supported by NSF Grant DMS-9423752.
Charles P. Boyer,B.M. Mann, and
Krzysztof Galicki.
Hypercomplex Structures from 3-Sasakian Structures. (J. reine angew. Math. 501
(1998) 115-141)
Postscript file (408K)pdf file
(449K) - posted
Sept 9, 1998. This work
was partially supported by NSF Grant DMS-9423752.
Charles P. Boyer,J.C. Hurtubise,
and R.J. Milgram.
Stability Theorems for Spaces of Rational Curves
(Int. J. Math. 12 (2001) 223-262)
Postscript file (905K)pdf file
(6642K)
revised version posted
May 26, 1999. This work
was partially supported by NSF Grant DMS-9423752 and DMS-9970904.
Selected Publications (1986-1998)
Conformal Duality and Compact Complex Surfaces, Math. Ann. 374, 517-526
(1986).
The Curved Twistor Construction for the Self-dual Einstein Equations - An
Integrable System, in Systemes Dynamiques Non-Lineaires
Int\'{e}grabilite: Et Comportement Qualitatif, pg. 23-39,
University of Montreal Press, 1986.
A Note on Hyperhermitian Four-Manifolds, Proc. Amer. Math. Soc.
102, 157-164 (1988).
Self-Dual and Anti-Self-Dual Hermitian Metrics on Compact Complex
Surfaces, Contemp. Math. 71, 105-114 (1988).
Homology Operations on Instantons, with B. Mann, J. Diff. Geom.
28, 423-455 (1988)
Monopoles, Non-Linear $\sigma$ Models, and Two-Fold Loop Spaces, with B.
Mann, Comm. Math. Phys. 115, 571-594 (1988).
Some Problems of Elementary Calculus in Superdomains, with O. A. Sanchez
Valenzuela, Aportaciones Matematicas Comunicaciones 5, 111-144
(1988).
Instantons and Homotopy, with B. Mann, in Proc. Int. Conf.
Homotopy Theory, Arcata (1986), L.N.M. 1370 Springer-Verlag, (1989).
Symmetries of the Self Dual Einstein Equations. I. The Infinite
Dimensional Symmetry Group and its Low Dimensional Subgroups, with P.
Winternitz, J. Math. Phys. 30, (1989) 1081-1094.
Quaternionic Lie Algebras, Hyperk\"{a}hler geometry, and Instantons, with
B.M. Mann, in Proc. of Annual Sem. of Can. Math. Soc., Lie Theory,
Differential Equations, and Representation Theory, (1990) 119-136.
Lie Supergroup Actions on Supermanifolds, with O. A. Sanchez Valenzuela,
Trans. Amer. Math. Soc., 323, (1991) 151-175.
On the Homology of $SU(n)$ Instantons, with B.M Mann and D. Waggoner,
Trans. Amer. Math. Soc. 323(2) (1991), 529-562.
The Atiyah Jones Conjecture, with J.C. Hurtubise, B.M. Mann, and R.J.
Milgram, Bull. Amer. Math. Soc. 26(2) (1992), 317-321.
The Hyperk\"ahler Geometry of the ADHM Construction and Quaternionic
Geometric Invariant Theory, with B.M. Mann, Proc. Symp. Pure Math. 54 (1993)
45-83.
The Topology of Instanton Moduli Spaces. I: The Atiyah-Jones
Conjecture, with J.C. Hurtubise, B.M. Mann, and R.J. Milgram, Ann.
of Math. 137 (1993) 561-609.
Algebraic Cycles and Infinite Loop Spaces, with H.B. Lawson, P.
Lima-Filho, B.M. Mann, and M.-L. Michelsohn, Invent. Math.
113 (1993) 373-388.
Quaternionic Reduction and Einstein Manifolds, with K. Galicki, and
B.M.Mann, Communications in Analysis and Geometry 1 (1993)
3-Sasakian Manifolds, with K. Galicki and B.M. Mann, Proc. Japan Acad.
69 Ser. A (1993) 335-340.
New Examples of Inhomogeneous Einstein Manifolds of Positive Scalar
Curvature, with K. Galicki and B.M. Mann, Mathematical Research
Letters 1 (1994) 115-121.
Topology of Holomorphic Maps into Generalized Flag Manifolds, with J.
Hurtubise, B.M. Mann, and R.J. Milgram, Acta Mathematica 173
(1994) 61-101.
The Geometry and Topology of 3-Sasakian Manifolds, with K. Galicki and
B.M. Mann. J. reine und Ange. Math. 455 (1994) 183-220.
Some New Examples of Compact Inhomogeneous Hypercomplex Manifolds, with
K. Galicki and B.M. Mann, Math. Research Letters 1 (1994) 531-538.
The Atiyah-Jones Conjecture, in a volume in Honor of Samuel
Gitler, Contemp. Math. 188 (1995) 51-56.
Quaternionic Geometry and 3-Sasakian Manifolds, with K. Galicki and
B.M. Mann, in the Proceedings of the Conference on Quaternionic Geometry in
Mathematics and Physics, SISSA, Trieste, ILAS/FM-6 (1996) 7-24.
Hypercomplex Structures on Stiefel Manifolds, with K. Galicki and B.M.
Mann. Ann. of Global Anal. and Geom. 14 (1996) 81-105.
On Strongly Inhomogeneous Einstein Manifolds, with K. Galicki and B.M.
Mann, Bull. London Math. Soc. 28 (1996) 401-408.
The Twistor Space of a 3-Sasakian Manifold, with K. Galicki,
Int. J. of Math. 8 (1997) 31-60.
Positive Einstein Manifolds with Arbitrary second Betti
Number, with K. Galicki, B.M. Mann, and E.G. Rees, Balkan Jour.
of Geom. and Its Appl. 1 (1996) 1-8.
Compact 3-Sasakian 7-Manifolds with Arbitrary second Betti
Number, with K. Galicki, B.M. Mann, and E.G. Rees, Invent. Math.
131 (1998) 321-344.
A Note on Smooth Toral Reductions of Spheres, with K. Galicki and
B.M. Mann, Manuscripta Math. 95 (1998) 149-158.