Coindex and rigidity of Einstein metrics on homogeneous Gray manifolds

Paul Schwahn

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arXiv · 2203.08005

Coindex and rigidity of Einstein metrics on homogeneous Gray manifolds

Paul Schwahn

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Abstract

Any $6$-dimensional strict nearly K\"ahler manifold is Einstein with positive scalar curvature. We compute the coindex of the metric with respect to the Einstein-Hilbert functional on each of the compact homogeneous examples. Moreover, we show that the infinitesimal Einstein deformations on $F_{1,2}=\mathrm{SU}(3)/T^2$ are not integrable into a curve of Einstein metrics.

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BibTeX RIS

Paul Schwahn. 2022-03-15. Coindex and rigidity of Einstein metrics on homogeneous Gray manifolds. https://arxiv.org/abs/2203.08005

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