A gap theorem for Ricci-flat 4-manifolds

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
Publication:	DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
Publisher:	ELSEVIER SCIENCE BV
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
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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