Articoli correlati a Foliations on Riemannian Manifolds
Sinossi
A first approximation to the idea of a foliation is a dynamical system, and the resulting decomposition of a domain by its trajectories. This is an idea that dates back to the beginning of the theory of differential equations, i.e. the seventeenth century. Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena. He emphasized the qualitative nature of these phenomena, thereby giving strong impetus to topological methods. A second approximation is the idea of a foliation as a decomposition of a manifold into submanifolds, all being of the same dimension. Here the presence of singular submanifolds, corresponding to the singularities in the case of a dynamical system, is excluded. This is the case we treat in this text, but it is by no means a comprehensive analysis. On the contrary, many situations in mathematical physics most definitely require singular foliations for a proper modeling. The global study of foliations in the spirit of Poincare was begun only in the 1940's, by Ehresmann and Reeb.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Contenuti
1. Introduction.- 2. Integrable forms.- 3. Foliations.- 4. Flat bundles and holonomy.- 5. Riemannian and totally geodesic foliations.- 6. Second fundamental form and mean curvature.- 7. Codimension one foliations.- 8. Foliations by level hypersurfaces.- 9. Infinitesimal automorphisms and basic forms.- 10. Flows.- 11. Lie foliations.- 12. Twisted duality.- 13. A comparison theorem.- References.- Appendix: Bibliography on foliations.- Index of notations.
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
- EditoreSpringer New York
- Data di pubblicazione1988
- ISBN 10 0387967079
- ISBN 13 9780387967073
- RilegaturaCopertina flessibile
- Numero di pagine260
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Foliations on Riemannian Manifolds (Universitext)
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New York: Springer-Verlag, 1988
ISBN 10: 0387967079
ISBN 13: 9780387967073
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Foliations on Riemannian Manifolds (Universitext)
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FOLIATIONS ON RIEMANNIAN MANIFOLDS
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Springer, 1988. [, 1988
ISBN 10: 0387967079
ISBN 13: 9780387967073
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Foliations on Riemannian Manifolds (Universitexts)
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Foliations on Riemannian Manifolds (Universitext)
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Foliations on Riemannian Manifolds
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Springer New York Mrz 1988, 1988
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ISBN 13: 9780387967073
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -A first approximation to the idea of a foliation is a dynamical system, and the resulting decomposition of a domain by its trajectories. This is an idea that dates back to the beginning of the theory of differential equations, i.e. the seventeenth century. Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena. He emphasized the qualitative nature of these phenomena, thereby giving strong impetus to topological methods. A second approximation is the idea of a foliation as a decomposition of a manifold into submanifolds, all being of the same dimension. Here the presence of singular submanifolds, corresponding to the singularities in the case of a dynamical system, is excluded. This is the case we treat in this text, but it is by no means a comprehensive analysis. On the contrary, many situations in mathematical physics most definitely require singular foliations for a proper modeling. The global study of foliations in the spirit of Poincare was begun only in the 1940's, by Ehresmann and Reeb. 260 pp. Englisch. Codice articolo 9780387967073
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Foliations on Riemannian Manifolds (Universitext)
Editore:
Springer New York 1988-01-01, 1988
ISBN 10: 0387967079
ISBN 13: 9780387967073
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Paperback. Condizione: New. Codice articolo 6666-IUK-9780387967073
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