Format:
Online Ressource (444 pages)
,
illustrations.
Edition:
Online-Ausg.
ISBN:
0122155041
,
9780122155048
Series Statement:
Pure and applied mathematics, a series of monographs and textbooks v. 10, pt. 4
Content:
Differential calculus on a differential manifold II : elementary global theory of first and second-order differential equations, elementary local theory of differential systems -- Lie groups and lie algebras -- Principal connections and Riemannian geometry
Note:
Translation of Elements d'Analyse, t.4. - Includes bibliographical references and index. - Print version record
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Front Cover; TREATISE ON ANALYSIS; Copyright Page; CONTENTS; Notation; Chapter XVlll. DIFFERENTIAL CALCULUS ON A DIFFERENTIAL MANIFOLD II. ELEMENTARY GLOBAL THEORY OF FIRST- AND SECOND- ORDER DIFFERENTIAL EQUATIONS. ELEMENTARY LOCAL THEORY OF DIFFERENTIAL SYSTEMS; 1. First-order differential equations on a differential manifold; 2. Flow of a vector field; 3. Second-order differential equations on a manifold; 4. Sprays and isochronous second-order equations; 5. Convexity properties of isochronous differential equations; 6. Geodesics of a connection
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7. One- parameter families of geodesics and Jacobi fields8. Fields of p-directions, Pfaffian systems, and systems of partial differential equations; 9. Differential systems; 10. Integral elements of a differential system; 11. Formulation of the problem of integration; 12. The Cauchy-Kowalewska theorem; 13. The Cartan-Kahler theorem; 14. Completely integrable Pfaffian systems; 15. Singular integral manifolds; characteristic manifolds; 16. Cauchy characteristics; 17. Examples: I. First-order partial differential equations; 18. Examples: II. Second-order partial differential equations
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Chapter XIX. LIE GROUPS AND LIE ALGEBRAS1. Equivariant actions of Lie groups on fiber bundles; 2. Actions of a Lie group G on bundles over G; 3. The infinitesimal algebra and the Lie algebra of a Lie group; 4. Examples; 5. Taylor's formula in a Lie group; 6. The enveloping algebra of the Lie algebra of a Lie group; 7. Immersed Lie groups and Lie subalgebras; 8. Invariant connections, one-parameter subgroups, and the exponential mapping; 9. Properties of the exponential mapping; 10. Closed subgroups of real Lie groups; 11. The adjoint representation. Normalizers and centralizers
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12. The Lie algebra of the commutator group13. Automorphism groups of Lie groups; 14. Semidirect products of Lie groups; 15. Differential of a mapping into a Lie group; 16. Invariant differential forms and Haar measure on a Lie group; 17. Complex Lie groups; Chapter XX. PRINCIPAL CONNECTIONS AND RIEMANNIAN GEOMETRY; 1. The bundle of frames of a vector bundle; 2. Principal connections on principal bundles; 3. Covariant exterior differentiation attached to a principal connection. Curvature form of a principal connection; 4. Examples of principal connections
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5. Linear connections associated with a principal connection6. The method of moving frames; 7. G-structures; 8. Generalities on pseudo-Riemannian manifolds; 9. The Levi-Civita connection; 10. The Riemann- Christoffel tensor; 11. Examples of Riemannian and pseudo-Riemannian manifolds; 12. Riemannian structure induced on a submanifold; 13. Curves in Riemannian manifolds; 14. Hypersurfaces in Riemannian manifolds; 15. The immersion problem; 16. The metric space structure of a Riemannian; 17. Sirictly geodesicallyconvex balls; 18. The metric manifolds; 19. Periodic geodesics
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20. First and second variation of arc length. Jacobi fields on a Riemannian manifold
Additional Edition:
ISBN 0122155041
Additional Edition:
Erscheint auch als Druck-Ausgabe Treatise on analysis New York : Academic Press, 1974
Language:
English
Keywords:
Electronic books
;
Electronic books
