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On Wilking's criterion for the Ricci flow by Gururaja, H. A.; Maity, Soma; Seshadri, Harish is a scholarly article available to read on EtoBox.

What is On Wilking's criterion for the Ricci flow about?

B Wilking has recently shown that one can associate a Ricci flow invariant cone of curvature operators $C(S)$, which are nonnegative in a suitable sense, to every $Ad_{SO(n,\C)}$ invariant subset $S \subset {\bf so}(n,\C)$. For curvature operators of a K\"ahler manifold of complex dimension $n$, one considers $Ad_{GL(n,\C)}$ invariant subsets $S \subset {\bf gl}(n,\C)$. In this article we show: (i) If $S$ is an $Ad_{SO(n,\C)}$ subset, then $C(S)$ is contained in the cone of curvature operators with nonnegative isotropic curvature and if $S$ is an $Ad_{GL(n,\C)}$ subset, then $C(S)$ is contained in the cone of K\"ahler curvature operators with nonnegative orthogonal bisectional curvature. (ii) If $S \subset {\bf so}(n,\C)$ is a closed $Ad_{SO(n,\C)}$ invariant subset and $C_+(S) \subset C(S)$ denotes the cone of curvature operators which are {\it 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 $C_+(S)$ also admits a metric with curvature operator in $C_+(S)$ (b) The normalized Ricci flow on any compact Riemannian manifold $M$ with curvature operator in $C_+(S)$ converges to

Author

Gururaja, H. A.; Maity, Soma; Seshadri, Harish

Published

2011

Language

EN