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HOMOGENEOUS HERMITIAN MANIFOLDS AND SPECIAL METRICS

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Abstract

We consider non-Kähler 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 Chern–Ricci tensor of the associated Chern connection is a positive multiple of the metric itself. The uniqueness and the property of being astheno-Kähler are also discussed.

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  1. Dipartimento di Matematica e Informatica “Ulisse Dini”, Università di Firenze, Viale Morgagni 67/A, 50100, Firenze, Italy

    FABIO PODESTÀ

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  1. FABIO PODESTÀ
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Correspondence to FABIO PODESTÀ.

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PODESTÀ, F. HOMOGENEOUS HERMITIAN MANIFOLDS AND SPECIAL METRICS. Transformation Groups 23, 1129–1147 (2018). https://doi.org/10.1007/s00031-017-9450-9

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