Stability and rigidity of normal homogeneous Einstein manifolds

Abstract: The stability of an Einstein metric is decided by the (non-)existence of small eigenvalues of the Lichnerowicz Laplacian on tt-tensors. In the homogeneous setting, harmonic analysis allows us to approach the computation of these eigenvalues. This easy on symmetric spaces, but considerably more difficult in the non-symmetric case. I review the case of irreducible symmetric spaces of compact type, prove the existence of a non-symmetric stable Einstein metric of positive scalar curvature, and give an outlook on how to investigate the normal homogeneous case. Furthermore, I explore the rigidity and infinitesimal deformability of homogeneous Einstein metrics.

Mathematics

Audience: researchers in the topic

Geometry Seminar - University of Florence

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