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Elementary Differential Geometry
The link between the physical world and its visualisation is geometry. This easy-to-read,
generously illustrated textbook presents an elementary introduction to differential
geometry with emphasis on geometric results. Avoiding formalism as much as possi-
ble, the author harnesses basic mathematical skills in analysis and linear algebra to
solve interesting geometric problems, which prepare students for more advanced study
in mathematics and other scientific fields such as physics puter science.
The wide range of topics includes curve theory, a detailed study of surfaces, cur-
vature, variation of area and minimal surfaces, geodesics, spherical and hyperbolic
geometry, the divergence theorem, triangulations, and the Gauss– theorem.
The section on cartography demonstrates the concrete importance of elementary dif-
ferential geometry in applications. Clearly developed arguments and proofs, colour
illustrations, and over 100 exercises and solutions make this book ideal for courses and
self-study. The only prerequisites are one year of undergraduate calculus and linear
algebra.
Christian Bär is Professor of Geometry in the Institute for Mathematics at the
University of Potsdam, Germany.
Elementary
Differential Geometry
Christian Ba¨r
Universität Potsdam, Germany
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore,
São Paulo, Delhi, Dubai, Tokyo
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
Information on this title: 0521896719
© C. Bär 2010
This publication is in copyright. Subject to statutory exception and to the
provision of relevant collective licensing agreements, no reproduction of any part
may take place without the written permission of Cambridge University Press.
First published in print format 2010
ISBN-13 978-0-511