Coindex and rigidity of Einstein metrics on homogeneous Gray manifolds

Paul Schwahn

Coindex and rigidity of Einstein metrics on homogeneous Gray manifolds

Differential Geometry 2022-08-25 v3

Authors: Paul Schwahn

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.

Keywords

einstein metrics coindex rigidity homogeneous gray manifolds nearly kahler einstein-hilbert functional infinitesimal deformations

Cite

@article{arxiv.2203.08005,
  title  = {Coindex and rigidity of Einstein metrics on homogeneous Gray manifolds},
  author = {Paul Schwahn},
  journal= {arXiv preprint arXiv:2203.08005},
  year   = {2022}
}

Comments

30 pages. v2: Shortened some elementary calculations. v3: Revised version

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