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arXiv · 1608.07968

Homogeneous Hermitian manifolds and special metrics

Fabio Podestà
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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.

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Fabio Podestà. 2016-08-29. Homogeneous Hermitian manifolds and special metrics. https://arxiv.org/abs/1608.07968

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