Positive sectional curvature is not preserved under the Ricci flow in dimensions seven and thirteen

2024/03/20 by David González-Álvaro, Masoumeh Zarei, González-Álvaro, David +1
Physics and Astronomy · Mathematics · Engineering · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Elasticity and Material Modeling

paper · pdf · doi:10.48550/arxiv.2403.13764

Abstract

We prove that there exist SU₃-invariant metrics on Aloff-Wallach spaces W⁷_{k1, k2}, as well as SU₅-invariant metrics on the Berger space B¹³, which have positive sectional curvature and evolve under the Ricci flow to metrics with non-positively curved planes.

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