Introduction to Differential Geometry

Description

Introduction to Differential Geometry has been planned for use, in an Honours Mathematics Course or as an introduction to the subject at postgraduate level.

This textbook gives all that is likely to be required at the undergraduate level and most of the material has in fact been taught to undergraduate. The book also gives a useful introduction to the methods of differential geometry or to tensor calculus for research students (e.g. in physics or engineering) who may wish to apply them.Part I is devoted to the classical theory of curves and surfaces, vector methods being used throughout. The last chapter dealing with global differential geometry of surface contains material which does not appear in any standard English text.Part II introduces the idea of a tensor, first in algebra and then in calculus. It gives the basic theory of absolute calculus and fundamentals of Riemannian geometry. The final chapter gives a brief account of the application of tensor methods to yield results previously obtained in Part I and some new results in addition.

Table of contents

PART ITHE THEORY OF CURVES AND SURFACES IN THREE DIMENTIONAL EUCLIDEAN SPACE
Chapter 1. The Theory of Space Curves
Chapter 2. The Metric: Local Intrinsic Properties of a Surface
Chapter 3. The Second Fundamental Form: Local Non-intrinsic Properties of a surface.Differential Geometry of the Surfaces in the Large
PART IIDIFFERENTIAL GEOMETRY OF n- DIMENSIONAL SPACE
Chapter 4. Tensor Algebra.
Chapter 5. Tensor Calculus.
Chapter 6. Riemannian Geometry
Chapter 7. Applications for Tensor Methods to Surface Theory.
Chapter 8. EXERCISES
Chapter 9. SUGGESTIONS FOR FURTHER READING