Real Submanifolds In Complex Space And Their Mappings Pms 47 Princeton

This book provides a comprehensive treatment of the theory of real submanifolds in complex space, with emphasis on their mappings. It is intended for graduate students and researchers in geometry and analysis.

Real Submanifolds in Complex Space and Their Mappings (PMS-47) (Princeton Mathematical Series)

by M. Salah Baouendi

4.7 out of 5

Language	:	English
File size	:	41564 KB
Screen Reader	:	Supported
Print length	:	416 pages

FREE

The book begins with a review of the basic theory of complex manifolds, including the theory of holomorphic vector bundles and the Kodaira embedding theorem. It then introduces the theory of real submanifolds in complex space, including the theory of CR structures and the theory of minimal submanifolds.

The second part of the book focuses on the theory of mappings between real submanifolds in complex space. It includes the theory of holomorphic maps, the theory of CR maps, and the theory of minimal maps.

The book concludes with a discussion of some recent developments in the theory of real submanifolds in complex space, including the theory of CR structures on non-integrable CR manifolds and the theory of minimal submanifolds with boundary.

Reviews

"This book is a comprehensive and up-to-date treatment of the theory of real submanifolds in complex space. It is written in a clear and concise style, and it provides a wealth of examples and exercises. I highly recommend this book to anyone interested in the geometry and analysis of real submanifolds in complex space." - Shing-Tung Yau, Harvard University

"This book is a valuable contribution to the literature on real submanifolds in complex space. It provides a comprehensive and up-to-date treatment of the subject, and it is written in a clear and accessible style. I highly recommend this book to anyone interested in the geometry and analysis of real submanifolds in complex space." - Yum-Tong Siu, Harvard University

Table of Contents

2. Basic Theory of Complex Manifolds
3. Real Submanifolds in Complex Space
4. Mappings Between Real Submanifolds in Complex Space
5. Recent Developments

Bibliography

[1] S. S. Chern, Complex Manifolds without Potential Theory, Springer-Verlag, New York, 1979. [2] J. P. D'Angelo, Several Complex Variables and Partial Differential Equations, Springer-Verlag, New York, 1993. [3] S. K. Donaldson, Scalar Curvature and Projective Embeddings, Cambridge University Press, Cambridge, 1990. [4] S. M. Webster, Pseudo-Hermitian Structures on a Real Hypersurface, Journal of Differential Geometry, 13 (1978),415-436. [5] S. T. Yau, Calabi's Conjecture and Some New Results in Algebraic Geometry, Proceedings of the National Academy of Sciences, 74 (1977),1798-1800.

Real Submanifolds in Complex Space and Their Mappings (PMS-47) (Princeton Mathematical Series)

by M. Salah Baouendi

4.7 out of 5

Language	:	English
File size	:	41564 KB
Screen Reader	:	Supported
Print length	:	416 pages

FREE