The Wong-Rosay type theorem for K\"ahler manifolds

Abstract

The Wong-Rosay theorem characterizes the strongly pseudoconvex domains of $\mathbb{C}^n$ by their automorphism groups. It has a lot of generalizations to other kinds of domains (for example, the weakly pseudoconvex domains). However, most of them are for domains of $\mathbb{C}^n$. In this note, we generalize the Wong-Rosay theorem to the simply-connected complete K\"{a}hler manifold with a negative sectional curvature. One aim of this note is to exhibit a Wong-Rosay type theorem of manifolds with holomorphic non-invariant metrics.