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Riemannian geometry in an orthogonal frame [[electronic resource] ] : from lectures delivered by Élie Cartan at the Sorbonne in 1926-1927 / / translated from Russian by Vladislav V. Goldberg ; foreword by S. S. Chern
| Riemannian geometry in an orthogonal frame [[electronic resource] ] : from lectures delivered by Élie Cartan at the Sorbonne in 1926-1927 / / translated from Russian by Vladislav V. Goldberg ; foreword by S. S. Chern |
| Autore | Cartan Elie <1869-1951.> |
| Pubbl/distr/stampa | River Edge, NJ, : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina |
516.3/73
516.373 |
| Altri autori (Persone) | FinikovS. P <1883-1964.> (Sergeĭ Pavlovich) |
| Soggetto topico |
Geometry, Riemannian
Geometry |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-94803-9
9786611948030 981-279-971-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents ; Foreword ; Translator's Introduction ; Preface to the Russian Edition ; PRELIMINARIES ; Chapter 1 Method of Moving Frames ; 1. Components of an infinitesimal displacement ; 2. Relations among 1-forms of an orthonormal frame
3. Finding the components of a given family of trihedrons 4. Moving frames ; 5. Line element of the space ; 6. Contravariant and covariant components ; 7. Infinitesimal affine transformations of a frame ; Chapter 2 The Theory of Pfaffian Forms ; 8. Differentiation in a given direction 9. Bilinear covariant of Frobenius 10. Skew-symmetric bilinear forms ; 11. Exterior quadratic forms ; 12. Converse theorems. Cartan's Lemma ; 13. Exterior differential ; Chapter 3 Integration of Systems of Pfaffian Differential Equations ; 14. Integral manifold of a system 15. Necessary condition of complete integrability 16. Necessary and sufficient condition of complete integrability of a system of Pfaffian equations ; 17. Path independence of the solution 18. Reduction of the problem of integration of a completely integrable system to the integration of a Cauchy system 19. First integrals of a completely integrable system ; 20. Relation between exterior differentials and the Stokes formula ; 21. Orientation ; Chapter 4 Generalization 22. Exterior differential forms of arbitrary order |
| Record Nr. | UNINA-9910454354303321 |
Cartan Elie <1869-1951.>
|
||
| River Edge, NJ, : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Riemannian geometry in an orthogonal frame [[electronic resource] ] : from lectures delivered by Élie Cartan at the Sorbonne in 1926-1927 / / translated from Russian by Vladislav V. Goldberg ; foreword by S. S. Chern
| Riemannian geometry in an orthogonal frame [[electronic resource] ] : from lectures delivered by Élie Cartan at the Sorbonne in 1926-1927 / / translated from Russian by Vladislav V. Goldberg ; foreword by S. S. Chern |
| Autore | Cartan Elie <1869-1951.> |
| Pubbl/distr/stampa | River Edge, NJ, : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina |
516.3/73
516.373 |
| Altri autori (Persone) | FinikovS. P <1883-1964.> (Sergeĭ Pavlovich) |
| Soggetto topico |
Geometry, Riemannian
Geometry |
| ISBN |
1-281-94803-9
9786611948030 981-279-971-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents ; Foreword ; Translator's Introduction ; Preface to the Russian Edition ; PRELIMINARIES ; Chapter 1 Method of Moving Frames ; 1. Components of an infinitesimal displacement ; 2. Relations among 1-forms of an orthonormal frame
3. Finding the components of a given family of trihedrons 4. Moving frames ; 5. Line element of the space ; 6. Contravariant and covariant components ; 7. Infinitesimal affine transformations of a frame ; Chapter 2 The Theory of Pfaffian Forms ; 8. Differentiation in a given direction 9. Bilinear covariant of Frobenius 10. Skew-symmetric bilinear forms ; 11. Exterior quadratic forms ; 12. Converse theorems. Cartan's Lemma ; 13. Exterior differential ; Chapter 3 Integration of Systems of Pfaffian Differential Equations ; 14. Integral manifold of a system 15. Necessary condition of complete integrability 16. Necessary and sufficient condition of complete integrability of a system of Pfaffian equations ; 17. Path independence of the solution 18. Reduction of the problem of integration of a completely integrable system to the integration of a Cauchy system 19. First integrals of a completely integrable system ; 20. Relation between exterior differentials and the Stokes formula ; 21. Orientation ; Chapter 4 Generalization 22. Exterior differential forms of arbitrary order |
| Record Nr. | UNINA-9910782279103321 |
|
Cartan Elie <1869-1951.>
|
||
| River Edge, NJ, : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Riemannian geometry in an orthogonal frame [[electronic resource] ] : from lectures delivered by Élie Cartan at the Sorbonne in 1926-1927 / / translated from Russian by Vladislav V. Goldberg ; foreword by S. S. Chern
| Riemannian geometry in an orthogonal frame [[electronic resource] ] : from lectures delivered by Élie Cartan at the Sorbonne in 1926-1927 / / translated from Russian by Vladislav V. Goldberg ; foreword by S. S. Chern |
| Autore | Cartan Elie <1869-1951.> |
| Pubbl/distr/stampa | River Edge, NJ, : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina |
516.3/73
516.373 |
| Altri autori (Persone) | FinikovS. P <1883-1964.> (Sergeĭ Pavlovich) |
| Soggetto topico |
Geometry, Riemannian
Geometry |
| ISBN |
1-281-94803-9
9786611948030 981-279-971-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents ; Foreword ; Translator's Introduction ; Preface to the Russian Edition ; PRELIMINARIES ; Chapter 1 Method of Moving Frames ; 1. Components of an infinitesimal displacement ; 2. Relations among 1-forms of an orthonormal frame
3. Finding the components of a given family of trihedrons 4. Moving frames ; 5. Line element of the space ; 6. Contravariant and covariant components ; 7. Infinitesimal affine transformations of a frame ; Chapter 2 The Theory of Pfaffian Forms ; 8. Differentiation in a given direction 9. Bilinear covariant of Frobenius 10. Skew-symmetric bilinear forms ; 11. Exterior quadratic forms ; 12. Converse theorems. Cartan's Lemma ; 13. Exterior differential ; Chapter 3 Integration of Systems of Pfaffian Differential Equations ; 14. Integral manifold of a system 15. Necessary condition of complete integrability 16. Necessary and sufficient condition of complete integrability of a system of Pfaffian equations ; 17. Path independence of the solution 18. Reduction of the problem of integration of a completely integrable system to the integration of a Cauchy system 19. First integrals of a completely integrable system ; 20. Relation between exterior differentials and the Stokes formula ; 21. Orientation ; Chapter 4 Generalization 22. Exterior differential forms of arbitrary order |
| Record Nr. | UNINA-9910809087603321 |
|
Cartan Elie <1869-1951.>
|
||
| River Edge, NJ, : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||