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

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"This book contains detailed solutions to 375 core exercises on differentiable manifolds, Lie groups, fiber bundles, and Riemannian geometry. It should be helpful to anyone who needs to aquire 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. The authors summarize the critical definitions and statements where incompatibility might occur. There is a very useful collection of formulas and tables at the end of the book." (Thomas Püttmann, Bochum, Zentralblatt Math, 2010) ` I am convinced that this book, which is moreover very nicely edited, will not only be appreciated by students and teachers, but also by many researchers who are interested in the fascinating field of differential geometry and its applications, and who seek a deeper insight into the matter and a better acquaintance with its basic techniques. '
Professor Frans Cantrijn in Mathematical Reviews (2002)
` This workbook is a really successful attempt to submit to the reader by very clever composed series of exercises and examples covering the whole area of manifolds, Lie groups, fibre bundles, and Riemannian geometry a deep understanding and feeling. The choice and order of the examples and exercises will be extraordinarily helpful and useful for any student or teacher of manifolds and differential geometry. '
from the Prologue by Professor Jürgen Eichhorn