The Foundations of Differential Geometry
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Foundations of Differential Geometry by Oswald Veblen
Book DescriptionThis 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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Book DetailsISBN: 9780521066747
(216mm x 140mm x 7mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 3-Jan-1932
Country of Publication: United Kingdom
Books By Author Oswald Veblen
Invariants of Quadratic Differential Forms, Paperback (June 2004)» View all books by Oswald Veblen
An early tract for students of differential geometry and mathematical physics.
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