Homogeneous locally conformally Kähler manifolds

Abstract

It is known that automorphism group $G$ of a compact homogeneous locally conformally Kähler manifold $M=G/H$ has at least a 1-dimensional center. We prove that the center of $G$ is at most 2-dimensional, and that if its dimension is 2, then $M$ is Vaisman and isometric to a mapping torus of an isometry of a homogeneous Sasakian manifold.

10 pages

Cited by in corpus (1)

• Homogeneous locally conformally Kaehler and Sasaki manifolds