Homogeneous almost Kähler Chern-Einstein manifolds of semisimple Lie groups

Dmitry Alekseevsky

created by chrysikos on 10 Sep 2019

13 sep 2019
-- 13:00

University of Hradec Králové

Abstract.

An almost Kähler manifold $(M, g, J)$, i.e. an almost Hermitian manifold with closed Kähler form $\omega$, is called Chern-Einstein manifold if the Ricci form $\rho$ of the Chern connection is proportional to the Kähler form, that is $\rho=\lambda\omega$, for some real number $\lambda$. In this talk we give a description of all homogeneous almost Kähler manifolds $(M=G/L, g, J)$ of a non-compact semi-simple Lie group $G$. We propose a general approach for classification of invariant Chern-Einstein structures on $M=G/L$ and give a complete description of homogeneous Chern-Einstein structures on the regular adjoint orbit of classical Lie groups $G$.
The talk is based on a joint work with Fabio Podesta