Steeb, Willi-Hans
Problems and solutions in differential geometry, lie series, differential forms, relativity, and applications - Indian edition - Singapore: World Scientific Publishing Co Pte Ltd., [c2020] - 284 p.
Chapter 1: Curves, Surfaces and Manifolds.
Chapter 2: Vector Fields, Lie Series and Lie Algebras.
Chapter 3: Metric Tensor Fields.
Chapter 4: Differential Forms and Applications.
Chapter 5: Lie Derivative 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.--- Summary provided by the publisher
9780000989024
Geometry, Differential.
Differential forms.
QA641 .S65
Problems and solutions in differential geometry, lie series, differential forms, relativity, and applications - Indian edition - Singapore: World Scientific Publishing Co Pte Ltd., [c2020] - 284 p.
Chapter 1: Curves, Surfaces and Manifolds.
Chapter 2: Vector Fields, Lie Series and Lie Algebras.
Chapter 3: Metric Tensor Fields.
Chapter 4: Differential Forms and Applications.
Chapter 5: Lie Derivative 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.--- Summary provided by the publisher
9780000989024
Geometry, Differential.
Differential forms.
QA641 .S65