PreprintarXiv licencearXiv
Compact homogeneous complex manifolds
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 Kähler (or Vaisman) cases, respectively, as well as existence results for balanced and Calabi-Yau with torsion metrics.
Related
- Global C2,α estimate for complex Monge--Ampère equations on compact Kähler manifolds
- Smoothness of bounded solutions to complex Hessian equations on compact Hermitian manifolds
- The interpolation method for the complex Hessian equation on compact Kähler manifolds
- The intersection of two real flag manifolds in a complex flag manifold, and the canonical form of a compact symmetric triad
- Resolvent bounds and eigenvalue estimates of generalized Schrödinger operators with complex potentials on compact manifolds
BibTeX
@misc{lauret2026compact,
title = {{Compact homogeneous complex manifolds}},
author = {Jorge Lauret},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.30747},
eprint = {2608.30747},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30747},
}
RIS
TY - UNPB
TI - Compact homogeneous complex manifolds
AU - Jorge Lauret
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2608.30747
UR - https://arxiv.org/abs/2608.30747
AB - 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 Kähler (or Vaisman) cases, respectively, as well as existence results for balanced and Calabi-Yau with torsion metrics.
ER -