Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers

This book is a collection of 375 completely solved exercises on differentiable manifolds, Lie groups, fibre bundles, and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools. It is the first book consisting of completely solved problems on differentiable manifolds, and therefore will be a complement to the books on theory. A 42-page formulary is included which will be useful as an aide-memoire, especially for teachers and researchers on these topics. The book includes 50 figures. Audience: The book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics, and some branches of engineering.

Table of Contents:
Differentiable manifolds.- Tensor Fields and Differential Forms.- Integration on Manifolds.- Lie Groups.- Fibre Bundles.- Riemannian Geometry.- Some Definitions and Theorems.- Some Formulas and Tables.

Review :
From the reviews: "This is a collection of solved problems on differentiable manifolds, Lie groups, and Riemannian geometry. ... There are plenty of pictures to accompany the problems, including a few in color. ... I suspect the book will be particularly useful to instructors who are not specialists in the subject; most of the results and problems here are likely to be familiar to those working in the field. I would certainly want to have this book on hand if I were to teach such a course." (Fernando Q. Gouvea, The Mathematical Association of America, April, 2010) "This book contains detailed solutions to 375 core exercises on differentiable manifolds, Lie groups, fiber bundles, and Riemannian geometry. ... helpful to anyone who needs to acquire a solid working technique in these fields and to students who have problems to illustrate concepts, methods, and theorems by examples. The notation is compatible with most standard textbooks, so that teachers might well refer to this book as a reference. ... There is a very useful collection of formulas and tables at the end of the book." (Thomas Puttmann, Zentralblatt MATH, Vol. 1183, 2010) "The present book provides a remedy for this dilemma, and does so in a very convincing manner. ... It also collects in its final chapters some fundamental results from these theories, as well as tables of important formulae. The material included here will help many teachers to improve their course material as well as students to come to grips with the necessary abstractions of the field." (M. Kunzinger, Monatshefte fur Mathematik, Vol. 163 (1), May, 2011) "This is an exercise book for students and teachers of a basic graduate level course in differential geometry. The expectation is that it will be used ... as a source for additional exercises and practice with solutions. ... Supplementary material at the end of the book includes a terse review of definitions, terminology, notation, and background results, along with an index of notations. ... use it as a source of homework or exam exercises." (Peter J. Olver, SIAM Review, Vol. 53 (1), 2011)