Format:
Online-Ressource (XXV, 617 p. 68 illus., 38 illus. in color, digital)
Edition:
2nd ed. 2013
ISBN:
9789400759527
Series Statement:
Problem Books in Mathematics
Content:
Differentiable manifolds -- Tensor Fields and Differential Forms -- Integration on Manifolds -- Lie Groups -- Fibre Bundles -- Riemannian Geometry -- Some Formulas and Tables.
Content:
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.
Note:
Description based upon print version of record
,
Differentiable manifolds -- Tensor Fields and Differential Forms -- Integration on Manifolds -- Lie Groups -- Fibre Bundles -- Riemannian Geometry -- Some Formulas and Tables.
,
1.8 Submersions. Quotient Manifolds1.9 The Tangent Bundle; 1.10 Vector Fields; 1.10.1 Integral Curves; 1.10.2 Flows; 1.10.3 Transforming Vector Fields; References; Further Reading; Chapter 2: Tensor Fields and Differential Forms; 2.1 Some Definitions and Theorems on Tensor Fields and Differential Forms; 2.2 Vector Bundles; 2.3 Tensor and Exterior Algebras. Tensor Fields; 2.4 Differential Forms. Exterior Product; 2.5 Lie Derivative. Interior Product; 2.6 Distributions and Integral Manifolds. Frobenius Theorem. Differential Ideals; References; Further Reading; Chapter 3: Integration on Manifolds
Additional Edition:
ISBN 9789400759510
Additional Edition:
Buchausg. u.d.T. Gadea, Pedro M. Analysis and algebra on differentiable manifolds Dordrecht : Springer, 2013 ISBN 9789048135639
Language:
English
Subjects:
Mathematics
Keywords:
Algebra
;
Analysis
;
Differenzierbare Mannigfaltigkeit
DOI:
10.1007/978-94-007-5952-7
URL:
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