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arXiv · 2510.19156

Compact, connected, complex manifolds that admit a compact transitive group of holomorphic automorphisms

Lei Ni·Nolan Wallach
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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.

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Lei Ni, Nolan Wallach. 2025-10-22. Compact, connected, complex manifolds that admit a compact transitive group of holomorphic automorphisms. https://arxiv.org/abs/2510.19156

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