Introduction to Differential Geometry and Riemannian Geometry / / Erwin Kreyszig.

• Superior document: Title is part of eBook package: De Gruyter University of Toronto Press eBook-Package Archive 1933-1999
• VerfasserIn: Kreyszig, Erwin,
• Place / Publishing House: Toronto : : University of Toronto Press, , [2019]; ©1968
• Year of Publication: 2019
• Language: English
• Series: Heritage
• Physical Description: 1 online resource (382 p.)

This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space and to n-dimensional Riemannian geometry. Based on Kreyszig's earlier book Differential Geometry, it is presented in a simple and understandable manner with many examples illustrating the ideas, methods, and results. Among the topics covered are vector and tensor algebra, the theory of surfaces, the formulae of Weingarten and Gauss, geodesics, mappings of surfaces and their applications, and global problems. A thorough investigation of Reimannian manifolds is made, including the theory of hypersurfaces. Interesting problems are provided and complete solutions are given at the end of the book together with a list of the more important formulae. Elementary calculus is the sole prerequisite for the understanding of this detailed and complete study in mathematics.

Table of Contents

Frontmatter -- Preface -- Contents -- Important Notations -- I. Preliminaries -- II. Theory Of Curves -- III. Notion Of A Surface. First Fundamental Form -- IV. Second Fundamental Form. Gaussian And Mean Curvature -- V. Tensors -- VI. Formulae Of Weingarten And Gauss -- VII. Geodesic Curvature. Geodesics -- VIII. Isometric Mapping Of Surfaces -- IX. Further Mappings Of Surfaces -- X. Topics From Global Differential Geometry -- XI. Absolute Differentiation And Connexions On Surfaces -- XII. Special Surfaces -- XIII. Foundations Of Riemannian Geometry -- XIV. Absolute Differentiation And Connexion -- XV. Further Properties Of Riemannian Manifolds -- XVI. Hypersurfaces -- Answers to Odd-Numbered Problems -- Collection Of Formulae -- Bibliography -- Index