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Science China Mathematics

, Volume 62, Issue 3, pp 569–584 | Cite as

Invariant Einstein metrics on generalized Wallach spaces

  • Zhiqi ChenEmail author
  • Yuriĭ Gennadievich Nikonorov
Articles
  • 32 Downloads

Abstract

Invariant Einstein metrics on generalized Wallach spaces have been classified except SO(k + l + m)/SO(k) × SO(l) × SO(m). In this paper, we first 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) × SO(l) × SO(m) admitting exactly two, three, or four invariant Einstein metrics up to a homothety.

Keywords

compact homogeneous space generalized Wallach space symmetric space homogeneous Riemannian metric Einstein metric Ricci flow 

MSC(2010)

53C20 53C25 53C30 

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Notes

Acknowledgements

This work was supported by Ministry of Education and Sciences of the Republic of Kazakhstan for 2015–2017 (Agreement N 299, February 12, 2015) (Grant No. 1452/GF4). The authors are grateful to the referees for helpful comments and suggestions that improved the presentation of this paper.

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical Sciences and LPMCNankai UniversityTianjinChina
  2. 2.Southern Mathematical Institute of Vladikavkaz Scientific Centre of the Russian Academy of SciencesVladikavkazRussia

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