Invariant Einstein metrics on generalized Wallach spaces

Zhiqi Chen; Yu. G. Nikonorov

doi:10.1007/s11425-017-9150-3

Invariant Einstein metrics on generalized Wallach spaces

Differential Geometry 2019-04-22 v2

Authors: Zhiqi Chen , Yu. G. Nikonorov

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Abstract

Invariant Einstein metrics on generalized Wallach spaces have been classified except $SO(k+l+m)/SO(k)\times SO(l)\times SO(m)$ . In this paper, we give a survey on the study of invariant Einstein metrics on generalized Wallach spaces, and prove that there are infinitely many spaces of the type $SO(k+l+m)/SO(k)\times SO(l)\times SO(m)$ admitting exactly two, three, or four Einstein invariant metrics up to a homothety.

Keywords

einstein metrics measure theory metric spaces

Cite

@article{arxiv.1511.02567,
  title  = {Invariant Einstein metrics on generalized Wallach spaces},
  author = {Zhiqi Chen and Yu. G. Nikonorov},
  journal= {arXiv preprint arXiv:1511.02567},
  year   = {2019}
}

Comments

18 pages, 3 figures, some technical details are added, accepted for publication in SCIENCE CHINA Mathematics

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