Kähler Metrics on G
نویسنده
چکیده
We study G-invariant Kähler metrics on G from the Hamiltonian point of view. As an application we show that there exist G × G-invariant Ricci-flat Kähler metrics on G for any compact semisimple Lie group G.
منابع مشابه
Totally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures
In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...
متن کاملKähler metrics on
We study G-invariant Kähler metrics on G from the Hamiltonian point of view. As an application we show that there exist G × G-invariant Ricci-flat Kähler metrics on G for any compact semisimple Lie group G.
متن کاملKähler Metrics of Constant Scalar Curvature on Hirzebruch Surfaces
It is shown that a Hirzebruch surface admits a Kähler metric (possibly indefinite) of constant scalar curvature if and only if its degree equals zero. There have been many extensive studies for positive-definite Kähler metrics of constant scalar curvature, especially, Kähler Einstein metrics and scalar-flat Kähler metrics, on existence, uniqueness, obstructions, and relationships with other not...
متن کاملBergman Metrics and Geodesics in the Space of Kähler Metrics on Toric Varieties
Geodesics on the infinite dimensional symmetric space H of Kähler metrics in a fixed Kähler class on a projective Kähler manifold X are solutions of a homogeneous complex Monge-Ampère equation in X×A, where A ⊂ C is an annulus. They are analogues of 1PS (one-parameter subgroups) on symmetric spaces GC/G. Donaldson, Arezzo-Tian and Phong-Sturm raised the question whether Monge-Ampère geodesics c...
متن کاملKähler Metrics Generated by Functions of the Time-like Distance in the Flat Kähler-lorentz Space
We prove that every Kähler metric, whose potential is a function of the timelike distance in the flat Kähler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local classification of the Kähler manifolds with the above mentioned metrics. New examples of Sasakian space forms are obtained as real hypersurfaces of a Kähler space form ...
متن کامل