Stability of (generalized) Einstein Metrics on aligned Homogeneous Spaces.

Abstract: Given two standard Einstein homogeneous spaces $G_i/K$, where each $G_i$ is a compact simple Lie group and $K$ is a closed subgroup of them satisfying certain additional conditions, we consider $M = G_1\times G_2/\Delta K$. Recently, Lauret and Will proved the existence of a generalized Einstein metric on any of these spaces. When $G_1=G_2=H$ they also studied the existence and classification of $H \times H$-invariant Einstein metrics on $M= H\times H/\Delta K$.

In this talk we will discuss the definition and properties of aligned homogeneous spaces with two factors, review the results obtained by Lauret and Will and establish the dynamical stability of generalized Einstein metrics as fixed points of the generalized Ricci flow on $M$. Additionally, we will explore the stability relative to the Hilbert action of non-diagonal Einstein metrics on $M=H\times H/\Delta K$ when $H/K$ is an irreducible symmetric space.

differential geometrygeometric topologymetric 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 Differential geometry.

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