Analysis and Algebra on Differentiable Manifolds

the long version

<p>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.</p><p>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.</p><p>A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics.</p><p>In this 2nd edition:<br>• 76 new problems <br>• a section devoted to a generalization of Gauss’ Lemma<br>• a short novel section dealing with some properties of the energy of Hopf vector fields<br>• an expanded collection of formulae and tables<br>• an extended bibliography</p><p>Audience</p><p>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.</p>