Geometry I: Basic Ideas and Concepts of Differential Geometry - Basic Ideas and Concepts of Differential Geometry (Encyclopedia of Mathematical Sciences Series Vol. 28) - R. V. Gamkrelidze, V. V Lychagin, A. M. Vinogradov (1991)
ISBN 0387519998
Subject Geometry, Differential
Publisher Springer-Verlag
Publication Date September 1991
Format Hardcover (243 x 160 mm)
Language e
Since the early work of Gauss and Riemann, differential geometry has grown into a vast network of ideas and approaches, encompassing local considerations such as differential invariants and jets as well as global ideas, such as Morse theory and characteristic classes. In this volume of the Encyclopaedia, the authors give a tour of the principal areas and methods of modern differential geomerty. The book is structured so that the reader may choose parts of the text to read and still take away a completed picture of some area of differential geometry. Beginning at the introductory level with curves in Euclidian space, the sections become more challenging, arriving finally at the advanced topics which form the greatest part of the book: transformation groups, the geometry of differential equations, geometric structures, the equivalence problem, the geometry of elliptic operators. Several of the topics are approaches which are now enjoying a resurgence, e.g. G-structures and contact geometry. As an overview of the major current methods of differential geometry, EMS 28 is a map of these different ideas which explains the interesting points at every stop. The authors' intention is that the reader should gain a new understanding of geometry from the process of reading this survey.
Personal Details
Collection Status In Collection
Index 852
Read It Yes
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Product Details
LoC Classification QA641 .A59313 1991
Dewey 516.3/6
Cover Price $139.00
No. of Pages 256
Written by D.V. Alekseevskij, V.V. Lychagin, and A.M. Vinogradov.