Compact, connected, complex manifolds that admit a compact transitive group of holomorphic automorphisms
Differential Geometry
2025-10-23 v1 Complex Variables
Abstract
The purpose of this paper is to develop a Lie algebraic approach to obtain new proofs of important results of H.-C. Wang, Tits and Wolf-Wang-Ziller on compact complex homogeneous manifolds emphasizing only those that admit a transitive compact group of biholomorphic transformations. The method only uses some standard results in Lie theory. The new approach provides a method of associating a canonical abelian Lie algebra with a given integrable complex structure on a compact Lie algebra which extends the earlier work of Samelson and Pittie.
Cite
@article{arxiv.2510.19156,
title = {Compact, connected, complex manifolds that admit a compact transitive group of holomorphic automorphisms},
author = {Lei Ni and Nolan Wallach},
journal= {arXiv preprint arXiv:2510.19156},
year = {2025}
}