Compact, connected, complex manifolds that admit a compact transitive group of holomorphic automorphisms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866914107616133120 |
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| author | Ni, Lei Wallach, Nolan |
| author_facet | Ni, Lei Wallach, Nolan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19156 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compact, connected, complex manifolds that admit a compact transitive group of holomorphic automorphisms Ni, Lei Wallach, Nolan Differential Geometry Complex Variables 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. |
| title | Compact, connected, complex manifolds that admit a compact transitive group of holomorphic automorphisms |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2510.19156 |