Problems and Solutions in Differential Geometry, Lie Series, Differential Forms, Relativity and Applications

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.

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Contents:

• Preface
• Notation
• Curves, Surfaces and Manifolds
• Vector Fields, Lie Series and Lie Algebras
• Metric Tensor Fields
• Differential Forms and Applications
• Lie Derivative and Applications
• Bibliography
• Index

Readership: Graduate students, lecturers and researchers in differential geometry and its applications.
Key Features:

• Probably the first Problems and Solutions book in differential geometry with applications in pure mathematics and mathematical physics
• Each chapter starts with an introduction giving definitions and outlining techniques and strategies required for problem solving
• Supplementary problems are also included