Homogeneous Hermitian manifolds and special metrics
Differential Geometry
2016-08-30 v1
Abstract
We consider non-Kaehler compact complex manifolds which are homogeneous under the action of a compact Lie group of biholomorphisms and we investigate the existence of special (invariant) Hermitian metrics on these spaces. We focus on a particular class of such manifolds comprising the case of Calabi-Eckmann manifolds and we prove the existence of an invariant Hermitian metric which is Chern-Einstein, namely whose second Ricci tensor of the associated Chern connection is a positive multiple of the metric itself. The uniqueness is also discussed.
Keywords
Cite
@article{arxiv.1608.07968,
title = {Homogeneous Hermitian manifolds and special metrics},
author = {Fabio Podestà},
journal= {arXiv preprint arXiv:1608.07968},
year = {2016}
}