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The Foundations of Differential Geometry : Cambridge Tracts in Mathematics (Paperback) - Oswald Veblen

The Foundations of Differential Geometry

Cambridge Tracts in Mathematics (Paperback)

Paperback Published: 3rd March 1932
ISBN: 9780521066747
Number Of Pages: 108

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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.

Preface
The arithmetic space of n dimensions
Geometries, groups and co-ordinate systems
Allowable co-ordinates
Cells and scalars
Tangent spaces
A set of axioms for differential geometry
Various Geometries
Index of definitions
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521066747
ISBN-10: 0521066743
Series: Cambridge Tracts in Mathematics (Paperback)
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 108
Published: 3rd March 1932
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 21.7 x 14.3  x 0.7
Weight (kg): 0.15

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