Differential Geometry by Heinrich W Guggenheimer

Differential Geometry by Heinrich W Guggenheimer

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.

Heinrich W. Guggenheimer, Polytechnic Institute of New York University, Brooklyn, NY, USA.

SKU	Nicht verfügbar
ISBN 13	9780486634333
ISBN 10	0486634337
Titel	Differential Geometry
Autor	Heinrich W Guggenheimer
Serie	Dover Books On Mathema 14tics
Buchzustand	Nicht verfügbar
Bindungsart	Paperback
Verlag	Dover Publications Inc.
Erscheinungsjahr	2003-03-28
Seitenanzahl	400
Hinweis auf dem Einband	Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden.