1.

Record Nr.

UNINA9910953586603321

Autore

Cartan Elie <1869-1951.>

Titolo

Riemannian geometry in an orthogonal frame : from lectures delivered by Elie Cartan at the Sorbonne in 1926-1927 / / translated from Russian by Vladislav V. Goldberg ; foreword by S. S. Chern

Pubbl/distr/stampa

River Edge, NJ, : World Scientific, c2001

ISBN

9786611948030

9781281948038

1281948039

9789812799715

9812799710

Edizione

[1st ed.]

Descrizione fisica

1 online resource (280 p.)

Altri autori (Persone)

FinikovS. P <1883-1964.> (Sergeĭ Pavlovich)

Disciplina

516.3/73

516.373

Soggetti

Geometry, Riemannian

Geometry

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Translated from the 1960 Russian ed., which was translated and edited from original lecture notes by S.P. Finikov as, Rimanova geometriya v orthogonalnom repere.

Nota di bibliografia

Includes bibliographical references and index.

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

Sommario/riassunto

Foreword by <i>S S</i> <i>Chern</i>   In 1926-27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of these Cartan's lectures and published them as a book entitled Riemannian Geometry in an Orthogonal Frame. This book has many innovations