Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds
Kobayashi-hyperbolic manifolds are an object of active research in complex geometry. In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimension
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Alexander Isaev
Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds
1902
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1902
Alexander Isaev
Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds
ABC
Author Alexander Isaev Australian National University Canberra ACT 0200 Australia e-mail: [email protected]
Library of Congress Control Number: 2006939004 Mathematics Subject Classification (2000): 32Y45, 32M05, 32M10 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-69151-0 Springer Berlin Heidelberg New York ISBN-13 978-3-540-69151-8 Springer Berlin Heidelberg New York DOI 10.1007/3-540-69151-0 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. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting by the author and SPi using a Springer LATEX macro package Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper
SPIN: 11963370
VA41/3100/SPi
543210
Preface
This book is based on a series of lectures that I gave at the Geometry and Analysis Seminar held in the Mathematical Sciences Institute of the Australian National University in October–November, 2005. For some time now I have been interested in characterizations of complex manifolds by their holomorphic automorphism groups, and my lectures summarized the results that I obtained in this direction (on some occasions jointly with S. Krantz and N. Kruzhilin) for the class of Kobayashi-hyperbolic manifolds during 2000–2005, with the majority of results produced in 2004–2005. Here I give a coherent exposition (that includes complete proofs) of results describing hyperbolic manifolds for which the automorphism group dimensions are “sufficiently high” (this will be made precise in Chap. 1). The classification problem for hyperbolic manifolds with high-dimensional automorphism group can be thought of as a complex-geometric analogue of that for Riemannian manifolds with high-dimensional isometry group, which inspired many results in the 1950’s-70’s. Although the methods presented in the book are almost entirely different from those utilized in the Riemannian case, there i
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