On the Steinness of a class of K\"ahler manifolds

Albert Chau; Luen-Fai Tam

On the Steinness of a class of K\"ahler manifolds

Differential Geometry 2007-08-21 v2 Analysis of PDEs

Authors: Albert Chau , Luen-Fai Tam

Abstract

Let $(M^n, g)$ be a complete non-compact K\"ahler manifold with non-negative and bounded holomorphic bisectional curvature. We prove that $M$ is holomorphically covered by a pseudoconvex domain in $\C^n$ which is homeomorphic to $\R^{2n}$ , provided $(M^n, g)$ has uniform linear average quadratic curvature decay.

Keywords

Kahler manifold Stein manifold holomorphic bisectional curvature pseudoconvex domain curvature decay

Cite

@article{arxiv.math/0610535,
  title  = {On the Steinness of a class of K\"ahler manifolds},
  author = {Albert Chau and Luen-Fai Tam},
  journal= {arXiv preprint arXiv:math/0610535},
  year   = {2007}
}

Comments

Theorem 1.1 has been improved, a new Theorem (Theorem 6.1) has been added

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