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Transactions of the American Mathematical Society

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ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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Sasakian-Einstein structures on $9\#(S^2\times S^3)$
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by Charles P. Boyer, Krzysztof Galicki and Michael Nakamaye PDF
Trans. Amer. Math. Soc. 354 (2002), 2983-2996 Request permission

Abstract:

We show that $\scriptstyle {9\#(S^2\times S^3)}$ 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 $\scriptstyle {b_2(M)\leq 8}$ 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
  • MR Author ID: 40590
  • Email: galicki@math.unm.edu
  • Michael Nakamaye
  • Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico
  • MR Author ID: 364646
  • Email: nakamaye@math.unm.edu
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 2983-2996
  • MSC (2000): Primary 53C25, 53C12, 14E30
  • DOI: https://doi.org/10.1090/S0002-9947-02-03015-5
  • MathSciNet review: 1897386