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arXiv · 2608.30747

Compact homogeneous complex manifolds

Jorge Lauret
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Abstract

We study both the complex and Hermitian geometry of C-spaces, i.e., compact homogeneous spaces M=G/K admitting a G-invariant complex structure. Some results on Hodge, Bott-Chern and Aeppli cohomologies are given. We also prove classification results in the pluriclosed, parallel Bismut torsion and locally conformally K\"ahler (or Vaisman) cases, respectively, as well as existence results for balanced and Calabi-Yau with torsion metrics.

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Jorge Lauret. 2026-08-31. Compact homogeneous complex manifolds. https://arxiv.org/abs/2608.30747

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