Transactions of the American Mathematical Society

Author(s): Charles P. Boyer; Krzysztof Galicki; Michael Nakamaye
Journal: Trans. Amer. Math. Soc. 354 (2002), 2983-2996.
MSC (2000): Primary 53C25, 53C12, 14E30
Posted: April 1, 2002
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 53C25, 53C12, 14E30

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: 10.1090/S0002-9947-02-03015-5
PII: S 0002-9947(02)03015-5
Received by editor(s): November 7, 2001
Posted: 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
Copyright of article: Copyright 2002, American Mathematical Society

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