Elementary Differential Geometry

• Andrew Pressley
Textbook

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

1. Front Matter
Pages I-IX
2. Andrew Pressley
Pages 1-21
3. Andrew Pressley
Pages 23-45
4. Andrew Pressley
Pages 47-57
5. Andrew Pressley
Pages 59-96
6. Andrew Pressley
Pages 97-121
7. Andrew Pressley
Pages 123-145
8. Andrew Pressley
Pages 147-169
9. Andrew Pressley
Pages 171-200
10. Andrew Pressley
Pages 201-228
11. Andrew Pressley
Pages 229-246
12. Andrew Pressley
Pages 247-280
13. Back Matter
Pages 281-332

Introduction

Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates.

Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum. Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times. Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there.

The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecturers, and for all others interested in the subject.

Andrew Pressley is Professor of Mathematics at King’s College London, UK.

The Springer Undergraduate Mathematics Series (SUMS) is a series designed for undergraduates in mathematics and the sciences worldwide. From core foundational material to final year topics, SUMS books take a fresh and modern approach and are ideal for self-study or for a one- or two-semester course. Each book includes numerous examples, problems and fully worked solutions.

Keywords

Curves and Surfaces Euclidean Geometry Gaussian curvature Geometry Minimal surface curvature differential geometry

Authors and affiliations

• Andrew Pressley
• 1
1. 1.Department of MathematicsKing’s CollegeLondonUK

Bibliographic information

• DOI https://doi.org/10.1007/978-1-4471-3696-5
• Copyright Information Springer-Verlag London 2001
• Publisher Name Springer, London
• eBook Packages
• Print ISBN 978-1-85233-152-8
• Online ISBN 978-1-4471-3696-5
• Series Print ISSN 1615-2085
• Buy this book on publisher's site