关键词: K?hler流形, Stein流形, 全纯函数, 负双截曲率, 紧性, 单连通性

Abstract: This paper investigated whether a complete，single connected Kähler manifold M with negative bisecting curvature was a Stein manifold. By reviewing the basic properties of Stein manifolds and Kähler manifolds， we focused on the construction method of holomorphic functions，the proof of compactness，and the single connectivity of manifolds， and then proved that such Kähler manifolds satisfied the definition of Stein manifolds.

Key words: K?hler manifolds, Stein manifolds, holomorphic functions, negative bisecting curvature, compactness, single connectivity