Non naturally reductive Einstein metrics on the orthogonal group via real flag manifolds

Abstract

We obtain new invariant Einstein metrics on the compact Lie groups $\SO(n)$ which are not naturally reductive. This is achieved by using the real flag manifolds $\SO(k_1+\cdots +k_p)/\SO(k_1)\times\cdots\times\SO(k_p)$ and by imposing certain symmetry assumptions in the set of all left-invariant metrics on $\SO(n)$.

14 pages

References in corpus (1)

• Classification of generalized Wallach spaces

Cited by in corpus (1)

• Non naturally reductive Einstein metrics on $\SU(N)$ via generalized flag manifolds