Geometry Revealed A Jacob's Ladder to Modern Higher Geometry
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is t
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Selected works of Marcel Berger R ESEARCH Le spectre d’une vari´et´e riemanniene (with Paul Gauduchon and Edmond Mazet), Springer, 1971 (Collaboratively under the pseudonym Arthur L. Besse) Manifolds all of whose geodesics are closed, Springer, 1978 (Collaboratively under the pseudonym Arthur L. Besse) Einstein Manifolds, Springer, 1978 P EDAGOGY AND POPULARIZATION Geometry I, II. Springer, 1987, 2009 Differential Geometry: Manifolds, Curves and Surfaces (with Bernard Gostiaux), Springer, 1987 “Peut-on d´efinir la g´eom´etrie aujourd’hui?”, in Results in Mathematics, vol. 40, pp. 37–87, 2001 A Panoramic View of Riemannian Geometry, Springer, 2003 ´ ADPF (Association pour la diffusion Cinq si`ecles de math´ematiques en France, Ed. de la pens´ee franc¸aise), 2005 Convexit´e dans le plan et dans l’espace: de la puissance et de la complexit´e d’une notion simple (with Pierre Damphousse), Ellipses, Paris, 2006 “Geometry in the 20th century”, 2002, in History of mathematics, edited by V.L. Hansen and J.J. Gray, Encyclopedia of Life Support Systems (EOLSS), Developed under the auspices of UNESCO, Eolss Publishers, Oxford, UK
M ARCEL B ERGER
Geometry Revealed A Jacob’s Ladder to Modern Higher Geometry
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Author Marcel Berger ´ Insitut des Hautes Etudes Scientifiques (IHES) Bures-sur-Yvette France
Translator Lester J. Senechal Professor Emeritus Department of Mathematics Mount Holyoke College South Hadley, MA 10475 USA [email protected]
Springer-Verlag thanks the original publishers of the figures for permission to reprint them in this book. We have made every effort to identify the copyright owners of all illustrations included in this book in order to obtain reprint permission. Some of our requests have however remained unanswered. We have inserted all sources and owners where known.
ISBN 978-3-540-70996-1 e-ISBN 978-3-540-70997-8 DOI 10.1007/978-3-540-70997-8 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010920837 Mathematics Subject Classification: 51-01, 01-01 c Springer-Verlag Berlin Heidelberg 2010 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 to prosecution under the German Copyright Law. 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. Cover design: Wmx design ´ Cover illustration: Le Songe de Jacob (detail), Nicolas Dipre (D’Ypres), Ecole d’Avignon, Mus´ee du c bp
