Coisotropic and polar actions on compact irreducible Hermitian symmetric spaces

Polar and coisotropic actions on Kaehler manifolds

The main result of this paper is that a polar action on a compact irreducible homogeneous Kaehler manifold is coisotropic. This is then used to give new examples of polar actions and to classify coisotropic and polar actions on quadrics.

Coisotropic and Polar actions on Complex Grassmannians

The main result of the paper is the complete classification of the compact connected Lie groups acting coisotropically on complex Grassmannians. This is used to determine the polar actions on the same manifolds.

Polar actions on Hermitian and quaternion-Kähler symmetric spaces

We analyze polar actions on Hermitian and quaternion-Kähler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries concerning the geometry of these actions. The results are independent of the classification of polar actions on Hermitian symmetric spaces. In the second part we prove that polar actions on Wolf spaces are quaternion-coisotropic and that isometric actions on these spaces admit an orbit of special type, analogous to the existence of a complex orbit for an isometric act…

恰当作用的约化原理

Reduction principles for proper actions

本文研究李群恰当作用的核心构造，证明极性与超极性等性质满足约化原理，并推广余迷向作用的刻画至恰当哈密顿作用及Kähler流形情形。

Equivariant realizations of Hermitian symmetric space of noncompact type

Let $M=G/K$ be a Hermitian symmetric space of noncompact type. We provide a way of constructing $K$-equivariant embeddings from $M$ to its tangent space $T_oM$ at the origin by using the polarity of the $K$-action. As an application, we reconstruct the $K$-equivariant holomorphic embedding so called the Harish-Chandra realization and the $K$-equivariant symplectomorphism constructed by Di Scala-Loi and Roos under appropriate identifications of spaces. Moreover, we characterize the holomorphic/symplectic embedding of $M$ by means of the polarity of the $K$-action. Furthermore, we show a special…

紧致Hermitian流形上$m$-次调和函数的极集

Polar sets for $m$-subharmonic functions on compact Hermitian manifolds

本文证明了紧致Hermitian流形上$(ω,m)$-次调和函数下水平集容量的精确衰减，并利用局部、全局容量及极值函数完整刻画了此类函数的极集。