Problems And Solutions In Differential Geometry, Lie Series, Differential Forms, Relativity And Applications

by Willi-hans Steeb

Overview

This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer-Cartan form, and the Lie derivative are covered.Readers will find useful applications to special and general relativity, Yang-Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry.

Product Details

ISBN-13:	9789813232969
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	12/18/2017
Pages:	296
Product dimensions:	6.00(w) x 9.00(h) x 0.62(d)

Table of Contents

Preface v

Notation ix

1 Curves, Surfaces and Manifolds 1

1.1 Notations and Definitions 1

1.2 Solved Problems 3

1.3 Supplementary Problems 51

2 Vector Fields, Lie Series and Lie Algebras 67

2.1 Notations and Definitions 67

2.2 Solved Problems 69

2.3 Supplementary Problems 96

3 Metric Tensor Fields 105

3.1 Notations and Definitions 105

3.2 Solved Problems 109

3.3 Supplementary Problems 142

4 Differential Forms and Applications 157

4.1 Notations and Definitions 157

4.2 Solved Problems 160

4.3 Supplementary Problems 217

5 Lie Derivative and Applications 235

5.1 Notations and Definitions 235

5.2 Solved Problems 237

5.3 Supplementary Problems 264

Bibliography 275

Index 281