Bhattacharya, Atreyee and Seshadri, Harish
(2015)
*A gap theorem for Ricci-flat 4-manifolds.*
In: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 40
.
pp. 269-277.

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## Abstract

Let (M, g) be a compact Ricci-fiat 4-manifold. For p is an element of M let K-max(P) (respectively K-min(p)) denote the maximum (respectively the minimum) of sectional curvatures at p. We prove that if K-max(p) <= -cK(min)(P) for all p is an element of M, for some constant c with 0 <= c < 2+root 6/4 then (M, g) is fiat. We prove a similar result for compact Ricci-flat Kahler surfaces. Let (M, g) be such a surface and for p is an element of M let H-max(p) (respectively H-min(P)) denote the maximum (respectively the minimum) of holomorphic sectional curvatures at p. If H-max(P) <= -cH(min)(P) for all p is an element of M, for some constant c with 0 <= c < 1+root 3/2, then (M, g) is flat. (C) 2015 Elsevier B.V. All rights reserved.

Item Type: | Journal Article |
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Additional Information: | Copy right for this article belongs to the ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS |

Keywords: | Einstein manifolds; Rigidity; Bochner formula |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Depositing User: | Id for Latest eprints |

Date Deposited: | 29 May 2015 05:34 |

Last Modified: | 29 May 2015 05:34 |

URI: | http://eprints.iisc.ac.in/id/eprint/51596 |

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