The aim of this paper is to prove the following result. PROPOSITION. Let G be a complex reducti¨e group, P and Q parabolic subgroups of G with P ; Q, and K a maximal compact subgroups of G. The K-in¨ariant Kahler᎐Einstein metric of GrP restricted to any fiber of the fibration GrP ª GrQ is again Kah
On index number and topology of flag manifolds
✍ Scribed by Jürgen Berndt; Sergio Console; Anna Fino
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 80 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0926-2245
No coin nor oath required. For personal study only.
✦ Synopsis
The k-number of a complex flag manifold and the index number of a real flag manifold is known to be equal to the sum of the Z 2 -Betti numbers of the manifold. We give an interpretation and alternative proofs of these results in the framework of symplectic topology and Morse theory.
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