Borel’s fixed point theorem for Kaehler manifolds and an application
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- by Andrew J. Sommese PDF
- Proc. Amer. Math. Soc. 41 (1973), 51-54 Request permission
Abstract:
A short proof of a generalization of the Borel fixed point theorem to the case of Kaehler manifolds is given and, as an application, a short proof of Wang’s theorem that compact simply connected homogeneous manifolds are projective and of the form $G/P$, where $G$ is a complex semisimple Lie group and $P$ is a parabolic subgroup.References
- A. Borel and R. Remmert, Über kompakte homogene Kählersche Mannigfaltigkeiten, Math. Ann. 145 (1961/62), 429–439 (German). MR 145557, DOI 10.1007/BF01471087
- Hsien-Chung Wang, Closed manifolds with homogeneous complex structure, Amer. J. Math. 76 (1954), 1–32. MR 66011, DOI 10.2307/2372397
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 51-54
- MSC: Primary 32M10; Secondary 53C30
- DOI: https://doi.org/10.1090/S0002-9939-1973-0322217-0
- MathSciNet review: 0322217