Quasi-potentials and Kähler–Einstein metrics on flag manifolds, II
نویسندگان
چکیده
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. 2003 Elsevier Inc. All rights reserved.
منابع مشابه
Warped product and quasi-Einstein metrics
Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...
متن کاملHigher canonical asymptotics of Kähler–Einstein metrics on quasi-projective manifolds
We derive a canonical asymptotic expansion up to infinite order of the Kähler–Einstein metric on a quasi-projective manifold, which can be compactified by adding a divisor with simple normal crossings. Characterized by the log filtration of the Cheng–Yau Hölder ring, the asymptotics are obtained by constructing an initial Kähler metric, deriving certain iteration formula and applying the isomor...
متن کاملInvariant Einstein Metrics on Flag Manifolds with Four Isotropy Summands
A generalized flag manifold is a homogeneous space of the form G/K, where K is the centralizer of a torus in a compact connected semisimple Lie group G. We classify all flag manifolds with four isotropy summands by the use of t-roots. We present new G-invariant Einstein metrics by solving explicity the Einstein equation. We also examine the isometric problem for these Einstein metrics. 2000 Mat...
متن کاملHermitian-einstein Metrics for Vector Bundles on Complete Kähler Manifolds
In this paper, we prove the existence of Hermitian-Einstein metrics for holomorphic vector bundles on a class of complete Kähler manifolds which include Hermitian symmetric spaces of noncompact type without Euclidean factor, strictly pseudoconvex domains with Bergman metrics and the universal cover of Gromov hyperbolic manifolds etc. We also solve the Dirichlet problem at infinity for the Hermi...
متن کاملInvariant Einstein Metrics on Generalized Flag Manifolds with Two Isotropy Summands
Let M = G/K be a generalized flag manifold, that is the adjoint orbit of a compact semisimple Lie group G. We use the variational approach to find invariant Einstein metrics for all flag manifolds with two isotropy summands. We also determine the nature of these Einstein metrics as critical points of the scalar curvature functional under fixed volume. 2000 Mathematics Subject Classification. Pr...
متن کامل