Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers: v. 23 (Kluwer Texts in the Mathematical Sciences) - Hardcover

Gadea, P.M.; Masque, J.Munoz

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9781402000270: Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers: v. 23 (Kluwer Texts in the Mathematical Sciences)

Hardcover

ISBN 10: 1402000278 ISBN 13: 9781402000270

Publisher: Kluwer Academic Publishers, 2001

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This book is a collection of 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 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. Audience: The book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics, and some branches of engineering.

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Review:

From the reviews of the first edition:

"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 J??rgen Eichhorn)

"This book is intended to cover the exercises of standard courses on analysis and algebra on differentiable manifolds ??? . There are quite many introductory books to modern differential geometry ??? . However, this book is the first one with completely solved problems on differentiable manifolds and therefore will be an excellent compliment to the books on theory. ??? We recommend this excellent book to both teachers and students of differential geometry and related topics." (G??bor Nagy, Acta Scientiarum Mathematicarum, Vol. 72, 2006)

About the Author:

Professor Pedro M. Gadea taught at the Universities of Santiago de Compostela and Valladolid, Spain. He is now a scientific researcher at the Instituto de F�sica Fundamental, CSIC, Madrid, Spain. He has published more than sixty research papers on several topics of differential geometry, algebraic topology and automatic speech recognition. He has also been advisor of four PhD theses. His current interests are in differential geometry, and specifically in Riemannian, K�hler, quaternion-K�hler and Spin(9) manifolds and structures, and their applications to supergravity. Outside of mathematics, his chief interests are history and minerals.

Professor J Mu�oz Masqu� taught at the University of Salamanca, Spain. He is currently a scientific researcher at the Instituto de Seguridad de la Informaci�n (ISI), CSIC, Madrid, Spain. He has written more than one hundred research articles on calculus of variations, Riemannian geometry, differential invariants, gauge theories, and public key cryptography, and he is currently studying on these topics. Outside of mathematics, his chief interests is Spanish poetry.

Professor Ihor Mykytyuk teaches at the Pedagogical University of Cracow, Poland. He is Head of Department at the Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, NASU, L'viv, Ukraine. He has published more than thirty research papers on several topics of differential geometry, Lie groups theory and integrable dynamical systems. He is a co-author of two monographs on these topics. His current interests are in differential geometry and Lie groups theory, and specifically in Riemannian, K�hler, hyper-K�hler and Spin(9) structures possessing rich groups of symmetries. Outside of mathematics, his main interests are history and bicycle travels.

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