The main topic of this book is the study of the interaction between two major subjects of modern mathematics, namely, the theory of Lie groups with its specific methods and ways of thinking as well as complex analysis with its analytic, algebraic and geometric aspects. More specifically, the author concentrates on the double role of Lie groups in complex analysis, namely, as groups of biholomorphic selfmaps of certain complex analytic objects on the one hand, and a special class of complex manifolds with an additional strong structure on the other. The book starts from the basics of this subject and introduces the reader into many fields of recent research.

A publication of Vieweg+Teubner. The AMS is exclusive distributor in North America. Vieweg+Teubner Publications are available worldwide from the AMS outside of Germany, Switzerland, Austria, and Japan.

Readership

Table of Contents

• Introduction
• Lie theory
• Automorphism groups
• Compact homogeneous manifolds
• Homogeneous vector bundles
• Function theory on homogeneous manifolds
• Concluding remarks
• Bibliography
• Index of notations
• Index of terminology