ENGLISH

Geometry I: basic ideas and concepts of differential geometry

By R.V. Gamkrelidze , E. Primrose , D.V. Alekseevskij , V.V. Lychagin , A.M. Vinogradov

Book information

Publisher
Springer-Verlag
Year
1991
ISBN
3540519998, 9783540519997, 0387519998
LCC
QA641 .A59313 1991
Open Library ID
OL1884192M
Language
english
Format
DJVU
Filesize
2 MB (2136211 bytes)
Series
Encyclopaedia of mathematical sciences 28
Edition
1
Pages
267\267
Library
Kolxo3
DPI
600
Scanned
yes
Time added
2009-07-20 03:45:11

Description

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.

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