Introduction to Differential Geometry and Riemannian Geometry / Erwin Kreyszig.

Format:

Book

Author/Creator:

Kreyszig, Erwin, author.

Series:

Mathematical expositions ; Number 16.

Heritage

Language:

English

Subjects (All):

Geometry, Differential.

Geometry, Riemannian.

Genre:

Electronic books.

Physical Description:

1 online resource (383 pages) : illustrations.

Place of Publication:

Toronto : University of Toronto Press, [2019]

Language Note:

In English.

Summary:

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.

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

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Mrz 2019)

ISBN:

9781487591052

1487591055

9781487589448

1487589441

OCLC:

1091661158