CR Submanifolds of Complex Projective Space
This book covers the necessary topics for learning the basic properties of complex manifolds and their submanifolds, offering an easy, friendly, and accessible introduction into the subject while aptly guiding the reader to topics of current research
- PDF / 1,891,608 Bytes
- 171 Pages / 451 x 702 pts Page_size
- 26 Downloads / 209 Views
vm
9
1
developments in mathematics
CR Submanifolds of Complex Projective Space
13
19
CR SUBMANIFOLDS OF COMPLEX PROJECTIVE SPACE
Developments in Mathematics VOLUME 19 Series Editor: Krishnaswami Alladi, University of Florida, U.S.A.
CR SUBMANIFOLDS OF COMPLEX PROJECTIVE SPACE
By
MIRJANA DJORIC´ University of Belgrade, Serbia MASAFUMI OKUMURA Saitama University, Japan
123
Mirjana Djori´c Faculty of Mathematics University of Belgrade 11000, Belgrade Serbia [email protected]
Masafumi Okumura Professor Emeritus Saitama University Saitama, 338-8570 Japan [email protected]
ISSN 1389-2177 ISBN 978-1-4419-0433-1 e-ISBN 978-1-4419-0434-8 DOI 10.1007/978-1-4419-0434-8 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009936206 Mathematics Subject Classification (2000): 53C15, 53C40, 53B20, 53B25, 53B35, 53C20, 53C25, 53C42, 53C55, 53D15 c Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 1
Complex manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2
Almost complex structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
3
Complex vector spaces, complexification . . . . . . . . . . . . . . . . . . . 13
4
K¨ ahler manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5
Structure equations of a submanifold . . . . . . . . . . . . . . . . . . . . . . 27
6
Submanifolds of a Euclidean space . . . . . . . . . . . . . . . . . . . . . . . . . 39
7
Submanifolds of a complex manifold . . . . . . . . . . . . . . . . . . . . . . . 41
8
The Levi form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
9
The principal circle bundle S2n+1 (Pn (C), S1 ) . . . . . . . . . . . . . . 57
10 Submersion and immersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 11 Hypersurfaces of a Riemannian manifold of constant curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 12 Hypersurfaces of a sphere . . . . . . .
Data Loading...
