An Introduction to Differential Geometry

by T. J. Willmore

Overview

A solid introduction to the methods of differential geometry and tensor calculus, this volume is suitable for advanced undergraduate and graduate students of mathematics, physics, and engineering. Rather than a comprehensive account, it offers an introduction to the essential ideas and methods of differential geometry.
Part 1 begins by employing vector methods to explore the classical theory of curves and surfaces. An introduction to the differential geometry of surfaces in the large provides students with ideas and techniques involved in global research. Part 2 introduces the concept of a tensor, first in algebra, then in calculus. It covers the basic theory of the absolute calculus and the fundamentals of Riemannian geometry. Worked examples and exercises appear throughout the text.

Product Details

ISBN-13:	9780486486185
Publisher:	Dover Publications
Publication date:	02/15/2012
Series:	Dover Books on Mathematics Series
Edition description:	Reprint
Pages:	334
Product dimensions:	5.30(w) x 8.40(h) x 0.90(d)

About the Author

The author of four influential books on differential geometry, T. J. Willmore (1919–2005) was a Professor at the University of Durham and Liverpool University. He is best remembered as the developer of a branch of differential geometry known as Willmore surfaces, an area with applications extending to particle physics and colloidal chemistry.

Table of Contents

Preface
I. The Theory of Space curves
II. The Metric: Local Intrinsic Properties of a Surface
III. The Second Fundamental Form: Local Non-Intrinsic Properties of a Surface
IV. Differential Geometry of Surfaces in the Large
V. Tensor Algebra
VI. Tensor Calculus
VII. Riemannian Geometry
VIII. Applications of Tensor Methods to Surface Theory
Exercises
Suggestions for Further Reading
Index