A CHARACTERIZATION OF Ck×(C*) FROM THE VIEWPOINT OF BIHOLOMORPHIC AUTOMORPHISM GROUPS

Title & Authors
A CHARACTERIZATION OF Ck×(C*) FROM THE VIEWPOINT OF BIHOLOMORPHIC AUTOMORPHISM GROUPS
Kodama, Akio; Shimizu, Satoru;

Abstract
We show that if a connected Stein manifold M of dimension n has the holomorphic automorphism group Aut(M) isomorphic to $\small{Aut(C^k {\times}(C^*)^{n - k})}$ as topological groups, then M itself is biholomorphically equivalent to $\small{C^k{\times}(C^*)^{n - k}}$. Besides, a new approach to the study of U(n)-actions on complex manifolds of dimension n is given.
Keywords
holomorphic automorphism groups;holomorphic equivalences;torus actions;
Language
English
Cited by
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