ENGLISH

The foundations of differential geometry

By Oswald Veblen , J. H. C. Whitehead

Book information

Publisher
Cambridge University Press
Year
1932
ISBN
0521066743, 9780521066747
Language
english
Format
DJVU
Filesize
1 MB (1418486 bytes)
Series
Tracts in Mathematics
Edition
1
Pages
105\105
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11

Description

This book contains a set of axioms for differential geometry and develops their consequences up to a point where a more advanced book might reasonably begin. Analytical operations with co-ordinate systems are continually used in differential geometry, a typical process being to 'choose a co-ordinate system such that ...' It is therefore natural to state the axioms in terms of an undefined class of 'allowable' co-ordinate systems, and to deduce the properties of the space from the nature of the transformations of co-ordinates permitted by the axioms. These earlier axioms are found to be adequate for the differential geometry of an open simply connected space, the most elementary theorems of which occupy the greater part of Chapters III-V. The more general axioms, in terms of allowable co-ordinate systems and without restrictions on the connectivity of the space, are given in Chapter IV.

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