The Lichnerowicz Laplacian on normal homogeneous spaces

Abstract: The Lichnerowicz Laplacian $\Delta_L$ is an interesting differential operator on Riemannian manifolds, generalizing the Hodge-de Rham Laplacian on differential forms to tensors of arbitrary type. It features prominently in the study of the linear stability of Einstein metrics.

Normal homogeneous spaces are a natural setting in which Casimir operators occur. In the 80s, Koiso studied the stability of symmetric spaces of compact type, utilizing the coincidence of $\Delta_L$ with a Casimir operator. Motivated by his and also the $G$-stability results of Lauret-Lauret-Will, we generalize Koiso's strategy to general normal homogeneous spaces.

Ultimately this approach is sufficient to provide many new non-symmetric examples of stable Einstein manifolds of positive scalar curvature.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

( paper | 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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