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

2025/10/22 by Lei Ni, Nolan R. Wallach, Ni, Lei +1
Mathematics · #Advanced Algebra and Geometry #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2510.19156

openalex publication_date 2025/10/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

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.

Citations

• Pluriclosed manifolds with parallel Bismut torsion
• A note on compact homogeneous manifolds with Bismut parallel torsion
• Bismut Kähler-like manifolds of dimension 4 and 5
• A classification of locally Chern homogeneous Hermitian manifolds
• The classification of naturally reductive homogeneous spaces in dimensions n ≤ 6
• Invariant Affine Connections on Homogeneous Spaces

Related

• Homogeneous Hypercomplex Structures II - Coset Spaces of compact Lie\n Groups
• A note on the automorphism group of a compact complex manifold
• Complexifying Lie group actions on homogeneous manifolds of non-compact dimension two
• Automorphisms of \mathbb C^k and associated compact complex manifolds
• Realizing Connected Lie Groups As Automorphism Groups Of Complex Manifolds