| Riemannian Geometry 1990. Corr. 2nd Edition Contributor(s): Gallot, Sylvestre (Author), Hulin, Dominique (Author), LaFontaine, Jacques (Author) |
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ISBN: 3540524010 ISBN-13: 9783540524014 Publisher: Springer OUR PRICE: $94.05 Product Type: Paperback Published: December 1990 * Not available - Not in print at this time * |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Analytic - Mathematics | Geometry - Differential - Mathematics | Topology - General |
| Dewey: 516.373 |
| LCCN: 90022646 |
| Series: Lecture Notes in Artificial Intelligence |
| Physical Information: 0.64" H x 6.14" W x 9.21" (0.94 lbs) 286 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: In this second edition, the main additions are a section devoted to surfaces with constant negative curvature, and an introduction to conformal geometry. Also, we present a -soft-proof of the Paul Levy-Gromov isoperimetric inequal- ity, kindly communicated by G. Besson. Several people helped us to find bugs in the. first edition. They are not responsible for the persisting ones Among them, we particularly thank Pierre Arnoux and Stefano Marchiafava. We are also indebted to Marc Troyanov for valuable comments and sugges- tions. INTRODUCTION This book is an outgrowth of graduate lectures given by two of us in Paris. We assume that the reader has already heard a little about differential manifolds. At some very precise points, we also use the basic vocabulary of representation theory, or some elementary notions about homotopy. Now and then, some remarks and comments use more elaborate theories. Such passages are inserted between *. In most textbooks about Riemannian geometry, the starting point is the local theory of embedded surfaces. Here we begin directly with the so-called "abstract" manifolds. To illustrate our point of view, a series of examples is developed each time a new definition or theorem occurs. Thus, the reader will meet a detailed recurrent study of spheres, tori, real and complex projective spaces, and compact Lie groups equipped with bi-invariant metrics. Notice that all these examples, although very common, are not so easy to realize (except the first) as Riemannian submanifolds of Euclidean spaces. |