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Differential Geometry

Guggenheimer, Heinrich Walter

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ISBN 10: 0486634337 / ISBN 13: 9780486634333
Published by Dover Publications, Inc., New York, U.S.A., 1977
Used Condition: As New Soft cover
From D. Nakii Press (Albuquerque, NM, U.S.A.)

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AS DESCRIBED BY THE AUTHOR."THE BOOK PRESUPPOSES ONLY A FAIR KNOWLEDGE OF MATRIX ALGEBRA AND OF ADVANCED CALCULUS OF FUNCTIONS OF SEVERAL REAL VARIABLES." CHIPS ON COVER. Bookseller Inventory # 000142

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Bibliographic Details

Title: Differential Geometry

Publisher: Dover Publications, Inc., New York, U.S.A.

Publication Date: 1977

Binding: Soft cover

Book Condition:As New

Dust Jacket Condition: Very Good

About this title

Synopsis:

This is a text of local differential geometry considered as an application of advanced calculus and linear algebra. The discussion is designed for advanced undergraduate or beginning graduate study, and presumes of readers only a fair knowledge of matrix algebra and of advanced calculus of functions of several real variables.
The author, who is a Professor of Mathematics at the Polytechnic Institute of New York, begins with a discussion of plane geometry and then treats the local theory of Lie groups and transformation groups, solid differential geometry, and Riemannian geometry, leading to a general theory of connections.
The author presents a full development of the Erlangen Program in the foundations of geometry as used by Elie Cartan as a basis of modern differential geometry; the book can serve as an introduction to the methods of E. Cartan. The theory is applied to give a complete development of affine differential geometry in two and three dimensions.
Although the text deals only with local problems (except for global problems that can be treated by methods of advanced calculus), the definitions have been formulated so as to be applicable to modern global differential geometry. The algebraic development of tensors is equally accessible to physicists and to pure mathematicians. The wealth of specific resutls and the replacement of most tensor calculations by linear algebra makes the book attractive to users of mathematics in other disciplines.

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