Homogeneous almost quaternion-Hermitian manifolds

Abstract

An almost quaternion-Hermitian structure on a Riemannian manifold is a reduction of the structure group of to . In this paper we show that a compact simply connected homogeneous almost quaternion-Hermitian manifold of non-vanishing Euler characteristic is either a Wolf space, or S-2 x S-2 , or the complex quadric SO(7)/U(3) .