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arXiv · 2410.13058

Ricci curvature and Einstein metrics on aligned homogeneous spaces

Jorge Lauret·Cynthia Will
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Abstract

Let $M=G/K$ be a compact homogeneous space and assume that $G$ and $K$ have many simple factors. We show that the topological condition of having maximal third Betti number, in the sense that $b_3(M)=s-1$ if $G$ has $s$ simple factors, so called {\it aligned}, leads to a relatively manageable algebraic structure on the isotropy representation, paving the way to the computation of Ricci curvature formulas for a large class of $G$-invariant metrics. As an application, we study the existence and classification of Einstein metrics on aligned homogeneous spaces.

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Jorge Lauret, Cynthia Will. 2024-10-16. Ricci curvature and Einstein metrics on aligned homogeneous spaces. https://arxiv.org/abs/2410.13058

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