Differential and Riemannian Geometry - 1st Edition - ISBN: 9781483231679, 9781483263984

Differential and Riemannian Geometry

1st Edition

Authors: Detlef Laugwitz
eBook ISBN: 9781483263984
Imprint: Academic Press
Published Date: 1st January 1965
Page Count: 250
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Description

Differential and Riemannian Geometry focuses on the methodologies, calculations, applications, and approaches involved in differential and Riemannian geometry.

The book first offers information on local differential geometry of space curves and surfaces and tensor calculus and Riemannian geometry. Discussions focus on tensor algebra and analysis, concept of a differentiable manifold, geometry of a space with affine connection, intrinsic geometry of surfaces, curvature of surfaces, and surfaces and curves on surfaces.

The manuscript then examines further development and applications of Riemannian geometry and selections from differential geometry in the large, including curves and surfaces in the large, spaces of constant curvature and non-Euclidean geometry, Riemannian spaces and analytical dynamics, and metric differential geometry and characterizations of Riemannian geometry.

The publication elaborates on prerequisite theorems of analysis, as well as the existence and uniqueness theorem for ordinary first-order differential equations and systems of equations and integrability theory for systems of first-order partial differential equations.

The book is a valuable reference for researchers interested in differential and Riemannian geometry.

Table of Contents


Preface to the German Edition

Translator's Preface

Author's Note

Chapter I Local Differential Geometry of Space Curves

1. Differential-Geometric Properties of Curves

2. The Complete System of Invariants for Space Curves

Chapter II Local Differential Geometry of Surfaces

3. Surfaces, and Curves on Surfaces

4. Intrinsic Geometry of Surfaces

5. Curvature of Surfaces

6. Special Topics in the Theory of Surfaces

Chapter III Tensor Calculus and Riemannian Geometry

7. The Concept of a Differentiable Manifold

8. Tensor Algebra

9. Tensor Analysis

10. The Geometry of a Space with Affine Connection

11. Foundations of Riemannian Geometry

Chapter IV Further Development and Applications of Riemannian Geometry

12. Spaces of Constant Curvature and Non-Euclidean Geometry

13. Mappings

14. Riemannian Spaces and Analytical Dynamics

15. Metric Differential Geometry and Characterization of Riemannian Geometry

Chapter V Selections from Differential Geometry in the Large

16. Curves in the Large

17. Surfaces in the Large

Appendix I From the History of Differential Geometry

Appendix II Some Prerequisite Theorems of Analysis

1. Existence and Uniqueness Theorem for Ordinary First-Order Differential Equations and Systems of Equations

2. Integrability Theory for Systems of First-Order Partial Differential Equations

3. From the Calculus of Variations

Appendix III Summary of Formulas

Theory of Curves

Theory of Surfaces

Index

Details

No. of pages:
250
Language:
English
Copyright:
© Academic Press 1965
Published:
Imprint:
Academic Press
eBook ISBN:
9781483263984

About the Author

Detlef Laugwitz