Positive sectional curvature and Ricci flow

Abstract: The preservation of positive curvature conditions under the Ricci flow has been an important ingredient in applications of the flow to solving problems in geometry and topology. Works by Hamilton and others established that certain positive curvature conditions are preserved under the flow, culminating in Wilking's unified, Lie algebraic approach to proving invariance of positive curvature conditions. Yet, some questions remain. In this talk, we describe $\sec > 0$ metrics on $S^4$ and $\mathbb{C}P^2$, which evolve under the Ricci flow to metrics with sectional curvature of mixed sign. The setting is that of metrics invariant under a Lie group action of cohomogeneity one. This is joint work with Renato Bettiol.

differential geometry

Audience: researchers in the topic

( video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Riemannian geometry.

The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, send a message to geometrywithsymmetries@gmail.com requiring it.

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