Homogeneous spaces with two equivalent isotropy summands develop positive Ricci curvature under Ricci flow

2026/08/03 by Eric Cochran, Arseny Mingajev, Lawrence Mouillé +1
Mathematics · #math.DG #msc:53E20 #msc:53C20 #msc:53C21 #msc:53C30

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arxiv created 2026/08/03 · arxiv updated 2026/08/05

Abstract

We study normalized Ricci flow on simply connected homogeneous spaces G/H for which the isotropy representation splits into exactly two equivalent irreducible subrepresentations. We prove that every G-invariant metric evolves to one with positive Ricci curvature, and that the family of G-invariant metrics with positive Ricci curvature is forward-invariant under the flow. The proof relies on the fact that the phase portrait of the family of fixed-volume G-invariant metrics can be explicitly visualized.

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