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<p>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 homogenous 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 integral complex structure on a compact Lie algebra which extends the earlier work of Samelson and Pittie.</p>

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Compact, Connected, Complex Manifolds That Admit a Compact Transitive Group of Holomorphic Automorphisms

  • 期刊论文

  • 发表日期：

    2025年10月11日

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  • Lei Ni,
  • Nolan Wallach

摘要

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 homogenous 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 integral complex structure on a compact Lie algebra which extends the earlier work of Samelson and Pittie.