Hyperbolic Complex Spaces
In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Carathéodory and Kobayas
- PDF / 40,123,387 Bytes
- 480 Pages / 439.37 x 666.142 pts Page_size
- 42 Downloads / 213 Views
Editors
S. S. Chern B. Eckmann P. de la Harpe H. Hironaka F. Hirzebruch N. Hitchin L. Hörmander M.-A. Knus A. Kupiainen J. Lannes G. Lebeau M. Ratner D. Serre Ya.G. Sinai N. J. A. Sloane J.Tits M. Waldschmidt S. Watanabe Managing Editors
M. Berger J. Coates S.R.S. Varadhan
Springer-Verlag Berlin Heidelberg GmbH
Shoshichi Kobayashi
Hyp erb olic
Complex Spaces With 8 Figures
Springer
Shoshichi Kobayashi Department of Mathematics University of California Berkeley, CA 94720 USA e-mail: [email protected]
Library of Congress Cataloging-in-Publication Data Kobayashi, Shoshichi, 1932Hyperbolic complex spaces / Shoshichi Kobayashi. p. cm. - (Grundlehren der mathematischen Wissenschaften, ISSN 0072-7830; 318) Includes bibliographical references and index. ISBN 978-3-642-08339-6 ISBN 978-3-662-03582-5 (eBook) DOI 10.1007/978-3-662-03582-5 1. Analytic spaces. 2. Holomorphic functions. 3. Distance geometry. 1. Title. 11. Series. QA331.K716 1998 515'.94-dc21 98-16060 CIP
Mathematics Subject Classification (1991): 32H20, 32H15, 32H25 (primary) 32H35, 32H02, 32H04, 32H30 (secondary)
ISSN 0072-7830 ISBN 978-3-642-08339-6 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1998 Originally published by Springer-Verlag Berlin Heidelberg New York in 1998 Softcover reprint of the hardcover 1st edition 1998 Cover design: MetaDesign plus GmbH, Berlin Typesetting: Typeset in LATEX by the author and reformatted by Kurt Mattes, Heidelberg, using a Springer TEX macro-package 41/3143-5 4 3 2 1 0 Printed on acid-free paper SPIN: 10573657
Table of Contents
Introduction
IX
Chapter 1. Distance Geometry 2 3 4
Pseudo-distances Degeneracy of Inner Pseudo-distances Mappings into Metric Spaces Norms and Indicatrices
Chapter 2. Schwarz Lemma and Negative Curvature 2 3 4 5
Schwarz Lemma . . . . . . . . . . Negatively Curved Riemann Surfaces Negatively Curved Complex Spaces Ricci Forms and Schwarz Lemma for Volume Elements Metrics in Jet Bundles . . . . . . . . . . . . . .
1 7
8 13 19 19 25 30 35
41
Chapter 3. Intrinsic Distances
49
1 2 3 4 5
49
Two Intrinsic Pseudo-distances Hyperbolicity ....... . Hyperbolic Imbeddings . . . . Relative Intrinsic Pseudo-distance Infinitesimal Pseudometric F x 6 Brody's Criteria for Hyperbolicity and Applications 7 Differential Geometrie Criteria for Hyperbolicity ....... . 8 Subvarieties of Quasi Tori ....... . 9 Theorem of Bloch-Ochiai 10 Projective Spaces with Hyperplanes Deleted 11 Deformati
