Homogeneous almost-Kähler manifolds and the Chern–Einstein equation

Abstract

Given a non-compact semisimple Lie group G we describe all homogeneous spaces G / L carrying an invariant almost-Kahler structure $$(\omega ,J)$$ . When L is abelian and G is of classical type, we classify all such spaces which are Chern–Einstein, i.e. which satisfy $$\rho = \lambda \omega $$ for some $$\lambda \in {\mathbb {R}}$$ , where $$\rho $$ is the Ricci form associated to the Chern connection.