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NON-COERCIVE RICCI FLOW INVARIANT CURVATURE CONES

Richard, Thomas and Seshadri, Harish (2015) NON-COERCIVE RICCI FLOW INVARIANT CURVATURE CONES. In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 143 (6). pp. 2661-2674.

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Official URL: http://arxiv.org/abs/1308.1190

Abstract

This note is a study of nonnegativity conditions on curvature preserved by the Ricci flow. We focus on a specific class of curvature conditions which we call non-coercive: These are the conditions for which nonnegative curvature and vanishing scalar curvature does not imply flatness. We show, in dimensions greater than 4, that if a Ricci flow invariant nonnegativity condition is satisfied by all Einstein curvature operators with nonnegative scalar curvature, then this condition is just the nonnegativity of scalar curvature. As a corollary, we obtain that a Ricci flow invariant curvature condition, which is stronger than a nonnegative scalar curvature, cannot be strictly satisfied by curvature operators (other than multiples of the identity) of compact Einstein symmetric spaces. We also investigate conditions which are satisfied by all conformally flat manifolds with nonnegative scalar curvature.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the AMER MATHEMATICAL SOC, 201 CHARLES ST, PROVIDENCE, RI 02940-2213 USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 01 Aug 2015 04:29
Last Modified: 01 Aug 2015 04:29
URI: http://eprints.iisc.ac.in/id/eprint/52004

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