On the classification of holomorphic flows and Stein surfaces

Abstract

Our main result implies the global linearization of a complete holomorphic vector field on a Stein surface N with having a singularity of type where .

Keywords:

• Stein manifold
• Holomorphic flow
• Holomorphic foliation

Keywords:

• 2000 Mathematics Subject Classifications: Primary: 32E10
• Secondary: 32S65
• 37F75
• 32M25

Acknowledgement

The author expresses gratitude to the anonymous referee for many valuable remarks and suggestions which helped in making this article much more readable and straight to the point.