On the stability of compact homogeneous Einstein manifolds

Abstract: After some quick preliminaries on the general stability theory of compact Einstein manifolds, we will focus on the homogeneous case and give a formula for the Lichnerowicz Laplacian of a G-invariant metric on a compact homogeneous space M=G/K, restricted to the subspace of G-invariant TT-tensors, which was obtained via the moving bracket approach.

As an application, we study the stability type of G-invariant Einstein metrics on M, which are known to be the critical points of the scalar curvature restricted to unit volume G-invariant metrics. The naturally reductive case presents some advantages.

This is joint work with Cynthia Will and Emilio Lauret.

Mathematics

Audience: researchers in the topic

Geometry Seminar - University of Florence

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