This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds.

The exercises go from elementary computations to rather sophisticated tools. Many of the definitions and theorems used throughout are explained in the first section of each chapter where they appear.

A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics.

In this 2nd edition: . 76 new problems . a section devoted to a generalization of Gauss' Lemma . a short novel section dealing with some properties of the energy of Hopf vector fields . an expanded collection of formulae and tables . an extended bibliography

Audience

This book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics and some branches of engineering with a rudimentary knowledge of linear and multilinear algebra.

Autorentext

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 Física 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, Kähler, quaternion-Kähler and Spin(9) manifolds and structures, and their applications to supergravity. Outside of mathematics, his chief interests are history and minerals.

Professor J Muñoz Masqué taught at the University of Salamanca, Spain. He is currently a scientific researcher at the Instituto de Seguridad de la Información (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, Kähler, hyper-Kähler and Spin(9) structures possessing rich groups of symmetries. Outside of mathematics, his main interests are history and bicycle travels.

Inhalt

Differentiable manifolds.- Tensor Fields and Differential Forms.- Integration on Manifolds.- Lie Groups.- Fibre Bundles.- Riemannian Geometry.- Some Formulas and Tables.