Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers (Problem Books in Mathematics)
| Author | : | |
| Rating | : | 4.25 (694 Votes) |
| Asin | : | 9400759517 |
| Format Type | : | paperback |
| Number of Pages | : | 618 Pages |
| Publish Date | : | 2017-04-06 |
| Language | : | English |
DESCRIPTION:
(Hurray!) There is a section on what happens if one drops the standard topological assumptions (Hausdorff and second-countable) in the definition of a differentiable manifold. This book is an excellent resource for teachers and students of these topics. Other changes include: The Einstein summation convention is no longer used. It collects such things as the general formula for stereographic projection, formulas for Lie derivatives and wedge products of differential forms, and lists of the classical groups and their Lie algebras. The material is presented in a clear and lucid way. A final chapter gives a collection of formulas and tables relevant to differential geometry. In particular, it can serve as a most helpful tool, both for students and teachers of a course on the subject. Each chapter starts with a brief overview of the main definitions, concepts and properties o
Excellent problem book on advanced Differential Geometry lim_bus This work is a perfect and helpful companion to most theoretical books dealing with manifolds, calculus on manifolds (Stokes's general integration theorem), Lie Groups, Fiber Bundles and Riemannian Geometry. There are practical questions in low dimensions, as well as theoretical exercises. The level is never too demanding, since the authors do not address to the connoisseur but to real people struggling to understand how to handle tensor fields, cartan exterior calculus, the Lie derivative a. Beverly S. Lau said Four Stars. The book gives very detailed and helpful work out of problems in differential geometry.
Professor Pedro M. Gadea taught at the Universities of Santiago de Compostela and Valladolid, Spain. 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. He has also been advisor of four PhD
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 e