Elementary Differential Geometry - 1st Edition - ISBN: 9781483231709, 9781483268118

Elementary Differential Geometry

1st Edition

Authors: Barrett O'Neill
eBook ISBN: 9781483268118
Imprint: Academic Press
Published Date: 1st January 1966
Page Count: 422
Tax/VAT will be calculated at check-out Price includes VAT (GST)
30% off
30% off
30% off
30% off
30% off
20% off
20% off
30% off
30% off
30% off
30% off
30% off
20% off
20% off
30% off
30% off
30% off
30% off
30% off
20% off
20% off
54.95
38.47
38.47
38.47
38.47
38.47
43.96
43.96
43.99
30.79
30.79
30.79
30.79
30.79
35.19
35.19
72.95
51.06
51.06
51.06
51.06
51.06
58.36
58.36
Unavailable
Price includes VAT (GST)
× DRM-Free

Easy - Download and start reading immediately. There’s no activation process to access eBooks; all eBooks are fully searchable, and enabled for copying, pasting, and printing.

Flexible - Read on multiple operating systems and devices. Easily read eBooks on smart phones, computers, or any eBook readers, including Kindle.

Open - Buy once, receive and download all available eBook formats, including PDF, EPUB, and Mobi (for Kindle).

Institutional Access

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.

Description

Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces.

The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry.

The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation.

The text is a valuable reference for students interested in elementary differential geometry.

Table of Contents


Preface

Introduction

Chapter I. Calculus on Euclidean Space

1. Euclidean Space

2. Tangent Vectors

3. Directional Derivatives

4. Curves in E3

5. 1-Forms

6. Differential Forms

7. Mappings

8. Summary

Chapter II. Frame Fields

1. Dot Product

2. Curves

3. The Frenet Formulas

4. Arbitrary-Speed Curves

5. Covariant Derivatives

6. Frame Fields

7. Connection Forms

8. The Structural Equations

9. Summary

Chapter III. Euclidean Geometry

1. Isometries of E3

2. The Derivative Map of an Isometry

3. Orientation

4. Euclidean Geometry

5. Congruence of Curves

6. Summary

Chapter IV. Calculus on a Surface

1. Surfaces in E3

2. Patch Computations

3. Differentiable Functions and Tangent Vectors

4. Differential Forms on a Surface

5. Mappings of Surfaces

6. Integration of Forms

7. Topological Properties of Surfaces

8. Manifolds

9. Summary

Chapter V. Shape Operators

1. The Shape Operator of M C E3

2. Normal Curvature

3. Gaussian Curvature

4. Computational Techniques

5. Special Curves in a Surface

6. Surfaces of Revolution

7. Summary

Chapter VI. Geometry of Surfaces in E3

1. The Fundamental Equations

2. Form Computations

3. Some Global Theorems

4. Isometries and Local Isometries

5. Intrinsic Geometry of Surfaces in E3

6. Orthogonal Coordinates

7. Integration and Orientation

8. Congruence of Surfaces

9. Summary

Chapter VII. Riemannian Geometry

1. Geometric Surfaces

2. Gaussian Curvature

3. Covariant Derivative

4. Geodesics

5. Length-Minimizing Properties of Geodesics

6. Curvature and Conjugate Points

7. Mappings that Preserve Inner Products

8. The Gauss-Bonnet Theorem

9. Summary

Bibliography

Answer to Odd-Numbered Exercises

Index

Details

No. of pages:
422
Language:
English
Copyright:
© Academic Press 1966
Published:
Imprint:
Academic Press
eBook ISBN:
9781483268118

About the Author

Barrett O'Neill

Barrett O'Neill is currently a Professor in the Department of Mathematics at the University of California, Los Angeles. He has written two other books in advanced mathematics.

Affiliations and Expertise

University of California, Los Angeles, California, U.S.A.