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On Wilking's criterion for the Ricci flow

Gururaja, HA and Maity, Soma and Seshadri, Harish (2013) On Wilking's criterion for the Ricci flow. In: Mathematische Zeitschrift, 274 (1-2). pp. 471-481.

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Official URL: http://dx.doi.org/10.1007/s00209-012-1079-8

Abstract

Wilking has recently shown that one can associate a Ricci flow invariant cone of curvature operators , which are nonnegative in a suitable sense, to every invariant subset . In this article we show that if is an invariant subset of such that is closed and denotes the cone of curvature operators which are positive in the appropriate sense then one of the two possibilities holds: (a) The connected sum of any two Riemannian manifolds with curvature operators in also admits a metric with curvature operator in (b) The normalized Ricci flow on any compact Riemannian manifold with curvature operator in converges to a metric of constant positive sectional curvature. We also point out that if is an arbitrary subset, then is contained in the cone of curvature operators with nonnegative isotropic curvature.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Springer.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Francis Jayakanth
Date Deposited: 27 Jun 2013 07:51
Last Modified: 27 Jun 2013 07:51
URI: http://eprints.iisc.ac.in/id/eprint/46750

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