LEADER 05155nam 2200661Ia 450 001 9910782279103321 005 20230607222123.0 010 $a1-281-94803-9 010 $a9786611948030 010 $a981-279-971-0 035 $a(CKB)1000000000537964 035 $a(EBL)1681703 035 $a(OCoLC)879025492 035 $a(SSID)ssj0000238239 035 $a(PQKBManifestationID)11228439 035 $a(PQKBTitleCode)TC0000238239 035 $a(PQKBWorkID)10222268 035 $a(PQKB)11743758 035 $a(WSP)00004808 035 $a(Au-PeEL)EBL1681703 035 $a(CaPaEBR)ebr10255809 035 $a(CaONFJC)MIL194803 035 $a(MiAaPQ)EBC1681703 035 $a(EXLCZ)991000000000537964 100 $a20020311d2001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aRiemannian geometry in an orthogonal frame$b[electronic resource] $efrom lectures delivered by E?lie Cartan at the Sorbonne in 1926-1927 /$ftranslated from Russian by Vladislav V. Goldberg ; foreword by S. S. Chern 210 $aRiver Edge, NJ $cWorld Scientific$dc2001 215 $a1 online resource (280 p.) 300 $aTranslated from the 1960 Russian ed., which was translated and edited from original lecture notes by S.P. Finikov as, Rimanova geometriya v orthogonal?nom repere. 311 $a981-02-4746-X 320 $aIncludes bibliographical references and index. 327 $aContents ; 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 327 $a3. 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 327 $a9. 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 327 $a15. 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 327 $a18. 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 327 $a22. Exterior differential forms of arbitrary order 330 $aForeword by S S Chern 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 606 $aGeometry, Riemannian 606 $aGeometry 615 0$aGeometry, Riemannian. 615 0$aGeometry. 676 $a516.3/73 676 $a516.373 700 $aCartan$b Elie$f1869-1951.$042832 701 $aFinikov$b S. P$g(Sergei? Pavlovich),$f1883-1964.$01563135 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910782279103321 996 $aRiemannian geometry in an orthogonal frame$93831329 997 $aUNINA