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

TL;DR

This paper extends the Wong-Rosay theorem, originally for domains in complex Euclidean space, to simply-connected complete Kähler manifolds with negative sectional curvature, broadening its applicability.

Contribution

It generalizes the Wong-Rosay theorem to a new class of Kähler manifolds with negative curvature, including those with non-invariant metrics.

Findings

Wong-Rosay theorem is extended to Kähler manifolds with negative sectional curvature.

The generalization includes manifolds with holomorphic non-invariant metrics.

Provides a new characterization of automorphism groups in this broader setting.

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.