| Differential Geometry Contributor(s): Guggenheimer, Heinrich W. (Author) |
|
 |
ISBN: 0486634337 ISBN-13: 9780486634333 Publisher: Dover Publications OUR PRICE: $16.16 Product Type: Paperback - Other Formats Published: June 1977 Annotation: Designed for advanced undergraduate or beginning graduate study, this text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; and development of the method of integral formulas for global differential geometry. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential |
| Dewey: 516.36 |
| LCCN: 76027496 |
| Series: Dover Books on Mathematics |
| Physical Information: 0.77" H x 5.62" W x 8.24" (0.93 lbs) 400 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |