TAILIEUCHUNG - Manifolds and Differential Geometry

Classical differential geometry is the approach to geometry that takes full advantage of the introduction of numerical coordinates into a geometric space. This use of coordinates in geometry was the essential insight of Rene Descartes that allowed the invention of analytic geometry and paved the way for modern differential geometry. The basic object in differential geometry (and differential topology) is the smooth manifold. This is a topological space on which a sufficiently nice family of coordinate systems or "charts" is defined. The charts consist of locally defined n-tuples of functions. These functions should be sufficiently independent of each other so as to allow each point in their common domain. | Manifolds and Differential Geometry Jeffrey M. Lee Graduate Studies in Mathematics Volume 107 American Mathematical Society Manifolds and Differential Geometry Jeffrey M. Lee Graduate Studies in Mathematics Volume 107 American Mathematical Society Providence Rhode Island EDITORIAL COMMITTEE David Cox Chair Steven G. Krantz Rafe Mazzeo Martin Scharlemann 2000 Mathematics Subject Classification. Primary 58A05 58A10 53C05 22E15 53C20 53B30 55R10 53Z05. For additional information and updates on this book visit WWW. ams. or g b o okpages gs m-107 Library of Congress Cataloging-in-Publication Data Lee Jeffrey M. 1956- Manifolds and differential geometry Jeffrey M. Lee. p. cm. Graduate studies in mathematics V. 107 Includes bibliographical references and index. ISBN 978-0-8218-4815-9 alk. paper 1. Geometry Differential. 2. Topological manifolds. 3. Riemannian manifolds. I. Title. 2009 6 dc22 2009012421 Copying and reprinting. Individual readers of this publication and nonprofit libraries acting for them are permitted to make fair use of the material such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews provided the customary acknowledgment of the source is given. Republication systematic copying or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department American Mathematical Society 201 Charles Street Providence Rhode Island 02904-2294 USA. Requests can also be made by e-mail to . 2009 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. @ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence .

• Vật lý
• Differentiable 1!lanifolds
• Euclidean Space
• Lie Groups
• The Tangent Structure
• Hypersurfaces
• Submersion