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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Sasakian-Einstein structures on $9\char93 (S^2\times S^3)$


Authors: Charles P. Boyer, Krzysztof Galicki and Michael Nakamaye
Journal: Trans. Amer. Math. Soc. 354 (2002), 2983-2996
MSC (2000): Primary 53C25, 53C12, 14E30
Published electronically: April 1, 2002
MathSciNet review: 1897386
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Abstract: We show that $\scriptstyle{9\char93 (S^2\times S^3)}$ admits an 8-dimensional complex family of inequivalent non-regular Sasakian-Einstein structures. These are the first known Einstein metrics on this 5-manifold. In particular, the bound $\scriptstyle{b_2(M)\leq8}$ which holds for any regular Sasakian-Einstein $\scriptstyle{M}$does not apply to the non-regular case. We also discuss the failure of the Hitchin-Thorpe inequality in the case of 4-orbifolds and describe the orbifold version.


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Additional Information

Charles P. Boyer
Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico
Email: cboyer@math.unm.edu

Krzysztof Galicki
Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico
Email: galicki@math.unm.edu

Michael Nakamaye
Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico
Email: nakamaye@math.unm.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03015-5
PII: S 0002-9947(02)03015-5
Received by editor(s): November 7, 2001
Published electronically: April 1, 2002
Additional Notes: During the preparation of this work the first two authors were partially supported by NSF grant DMS-9970904, and third author by NSF grant DMS-0070190
Article copyright: © Copyright 2002 American Mathematical Society