Almost Hermitian homogeneous structures

Abstract

Let (M, g, J) be an almost Hermitian manifold. More precisely, M is a ∞ differentiable manifold of dimension 2n, J is an almost complex structure on M, i.e. it is a tensor field of type (1, 1) such thatfor any X∈(M), ((M) is the Lie algebra of ∞ vector fields on M), and g is a Riemannian metric compatible with J, i.e.