Quasi-potentials and Kähler–Einstein Metrics on Flag Manifolds

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

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 com...

Families of (1,2)-symplectic Metrics on Full Flag Manifolds

Invariant 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...

Quasi-fuchsian 3-manifolds and Metrics on Teichm¨uller Space

An almost Fuchsian 3-manifold is a quasi-Fuchsian manifold which contains an incompressible closed minimal surface with principal curvatures in the range of (−1, 1). Such a 3-manifold M admits a foliation of parallel surfaces, whose locus in Teichmüller space is represented as a path γ, we show that γ joins the conformal structures of the two components of the conformal boundary of M . Moreover...

On Riemannian nonsymmetric spaces and flag manifolds

In this work we study riemannian metrics on flag manifolds adapted to the symmetries of these homogeneous nonsymmetric spaces(. We first introduce the notion of riemannian Γ-symmetric space when Γ is a general abelian finite group, the symmetric case corresponding to Γ = Z2. We describe and study all the riemannian metrics on SO(2n + 1)/SO(r1) × SO(r2) × SO(r3) × SO(2n + 1 − r1 − r2 − r3) for w...