Format:
Online Ressource (xvii, 388 pages)
Edition:
Online-Ausg.
ISBN:
0122155033
,
9780122155031
Series Statement:
Pure and applied mathematics v. 10, pt. 3
Content:
Differential manifolds -- Differential calculus on a differential manifold I : distributions and differential operators
Note:
Includes bibliographical references and index. - Print version record
,
Front Cover; Treatise on Analysis; Copyright Page; Contents; Notation; Chapter XVI. DIFFERENTIAL MANIFOLDS; 1. Charts, atlases, manifolds; 2. Examples of differential manifolds. Diffeomorphisms; 3. Differentiable mappings; 4. Differentiable partitions of unity; 5. Tangent spaces, tangent linear mappings, rank; 6. Products of manifolds; 7. Immersions, submersions, subimmersions; 8. Submanifolds; 9. Lie groups; 10. Orbit spaces and homogeneous spaces; 11. Examples: unitary groups, Stiefel manifolds, Grassmannians, projective spaces; 12. Fibrations
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13. Definition of fibrations by means of charts14. Principal fiber bundles; 15. Vector bundles; 16. Operations on vector bundles; 17. Exact sequences, subbundles, and quotient bundles; 18. Canonical morphisms of vector bundles; 19. Inverse image of a vector bundle; 20. Differential forms; 21. Orientable manifolds and orientations; 22. Change of variables in multiple integrals. Lebesgue measures; 23. Sard's theorem; 24. Integral of a differential n-form over an oriented pure manifold of dimension n; 25. Embedding and approximation theorems. Tubular neighborhoods
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26. Differentiable homotopies and isotopies27. The fundamental group of a connected manifold; 28. Covering spaces and the fundamental group; 29. The universal covering of a differential manifold; 30. Covering spaces of a Lie group; Chapter XVll. DIFFERENTIAL CALCULUS ON A DIFFERENTIAL MANIFOLD; 1. The spaces &(r)(U) (U open in Rn); 2. Spaces of C8- (resp. Cr) sections of vector bundles; 3. Currents and distributions; 4. Local definition of a current. Support of a current; 5. Currents on an oriented manifold. Distributions on R""; 6. Real distributions. Positive distributions
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7. Distributions with compact support8. The weak topology on spaces of distributions; 9. Example: finite parts of divergent integrals; 10. Tensor products of distributions; 11. Convolution of distributions on a Lie group; 12. Regularization of distributions; 13. Differential operators and fields of point-distributions; 14. Vector fields as differential operators; 15. The exterior differential of a differential p-form; 16. Connections in a vector bundle; 17. Differential operators associated with a connection; 18. Connections on a differential manifold; 19. The covariant exterior differential
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20. Curvature and torsion of a connectionAppendix: Multilinear Algebra; 8. Modules. free modules; 9. Duality for free modules; 10. Tensor products of free modules; 11. Tensors; 12. Symmetric and antisymmetric tensors; 13 The exterior algebra; 14 Duality in the exterior algebra; 15. IInterior Products; 16. Nondegenerate alternating bilinear forms. symplectic groups; 17. The symmetric algebra; 18. Derivations and antiderivations of graded algebras; 19. Lie algebras; References; Index
Additional Edition:
ISBN 0122155033
Additional Edition:
Erscheint auch als Druck-Ausgabe Treatise on analysis. 3 New York, NY : Academic Press, 1972
Language:
English
Keywords:
Electronic books
;
Electronic books
