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Quasi-potentials and Kähler–Einstein metrics on flag manifolds, II

✍ Scribed by Hassan Azad; Indranil Biswas

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 208 KB
Volume: 269
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00500-3

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✦ Synopsis

For a homogeneous space G/P , where P is a parabolic subgroup of a complex semisimple group G, an explicit Kähler-Einstein metric on it is constructed. The Einstein constant for the metric is 1. Therefore, the intersection number of the first Chern class of the holomorphic tangent bundle of G/P coincides with the volume of G/P with respect to this Kähler-Einstein metric, thus enabling us to compute volume for this metric and for all Kählerian metrics on G/P invariant under the action of a maximal compact subgroup of G.

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Quasi-potentials and Kähler–Einstein Met

Quasi-potentials and Kähler–Einstein Metrics on Flag Manifolds

✍ H. Azad; R. Kobayashi; M.N. Qureshi 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 191 KB

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