Invariant Einstein metrics on generalized Wallach spaces

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.

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

References in corpus (1)

• Invariant Einstein metrics on Ledger-Obata spaces

Cited by in corpus (2)

• On locally homogeneous pseudo-Riemannian compact einstein manifolds
• Homogeneous Einstein metrics on non-Kähler C-spaces