LEADER 04980nam 2200613 a 450 001 9910877124903321 005 20200520144314.0 010 $a1-283-28111-2 010 $a9786613281111 010 $a1-118-03263-2 010 $a1-118-03088-5 035 $a(CKB)2550000000052728 035 $a(EBL)694624 035 $a(OCoLC)761321852 035 $a(SSID)ssj0000535330 035 $a(PQKBManifestationID)11359086 035 $a(PQKBTitleCode)TC0000535330 035 $a(PQKBWorkID)10522617 035 $a(PQKB)10816127 035 $a(MiAaPQ)EBC694624 035 $a(PPN)250683997 035 $a(EXLCZ)992550000000052728 100 $a19960628d1996 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aConformal differential geometry and its generalizations /$fMaks A. Akivis, Vladislav V. Goldberg 210 $aNew York $cWiley$dc1996 215 $a1 online resource (404 p.) 225 1 $aPure and applied mathematics 300 $a"A Wiley-Interscience publication." 311 $a0-471-14958-6 320 $aIncludes bibliographical references (p. 323-354) and indexes. 327 $aConformal Differential Geometry and Its Generalizations; Contents; Introduction; CHAPTER 1 CONFORMAL AND PSEUDOCONFORMAL SPACES; 1.1 Conformal transformations and conformal spaces; 1.2 Moving frames in a conformai space; 1.3 Pseudoconformal spaces; 1.4 Examples of pseudoconformal spaces; Notes; CHAPTER 2 HYPERSURFACES IN CONFORMAL SPACES; 2.1 Fundamental objects and tensors of a hypersurface; 2.2 Invariant normalization of hypersurfaces; 2.3 The rigidity theorem and the fundamental theorem; 2.4 Curvature lines of a hypersurface; 2.5 Geometric problems connected with the tensor cij; Notes 327 $aCHAPTER 3 SUBMANIFOLDS IN CONFORMAL AND PSEUDOCONFORMAL SPACES3.1 Geometry of a submanifold in a conformai space; 3.2 Submanifolds carrying a net of curvature lines; 3.3 Submanifolds in a pseudoconformal space; 3.4 Line submanifolds of a three-dimensional projective space; Notes; CHAPTER 4 CONFORMAL, STRUCTURES ON A DIFFERENTIABLE MANIFOLD; 4.1 A manifold with a conformal structure; 4.2 Weyl connections and Riemannian metrics compatible with a conformal structure; 4.3 A conformal structure on submanifolds of a conformal space; 4.4 A conformal structure on a hypersurface of a projective space 327 $aNotesCHAPTER 5 THE FOUR-DIMENSIONAL CONFORMAL STRUCTURES; 5.1 Structure equations of the CO(2, 2)-structure; 5.2 The (70(1, 3)-structure and the CO(4, 0)-structure; 5.3 The Hodge operator; 5.4 Completely isotropic submanifolds of four-dimensional conformal structures; 5.5 Four-dimensional webs and CO(2, 2)-structures; 5.6 Conformal structures of some metrics in general relativity; 5.7 Conformal structures on a four-dimensional hypersurface; Notes; CHAPTER 6 GEOMETRY OF THE GRASSMANN MANIFOLD; 6.1 Analytic geometry of the Grassmannian and the Grassmann mapping 327 $a6.2 Geometry of the Grassmannian G(l, 4)6.3 Differential geometry of the Grassmannian; 6.4 Submanifolds of the Grassmannian G(m, n); 6.5 Normalization of the Grassmann manifold; 6.6 Homogeneous normalization of the Grassmann manifold; Notes; CHAPTER 7 MANIFOLDS ENDOWED WITH ALMOST GRASSMANN STRUCTURES; 7.1 Almost Grassmann structures on a differentiable manifold; 7.2 Structure equations and torsion tensor of an almost Grassmann manifold; 7.3 The complete structure object of an almost Grassmann manifold; 7.4 Manifolds endowed with semiintegrable almost Grassmann structures 327 $a7.5 Multidimensional [p + l)-webs and almost Grassmann structures associated with them7.6 Grassmann (p + l)-webs; 7.7 Transversally geodesic and isoclinic (p + l)-webs; 7.8 Grassmannizable d-webs; Notes; Bibliography; Symbols Frequently Used; Author Index; Subject Index 330 $aComprehensive coverage of the foundations, applications, recent developments, and future of conformal differential geometryConformal Differential Geometry and Its Generalizations is the first and only text that systematically presents the foundations and manifestations of conformal differential geometry. It offers the first unified presentation of the subject, which was established more than a century ago. The text is divided into seven chapters, each containing figures, formulas, and historical and bibliographical notes, while numerous examples elucidate the necessary theory.C 410 0$aPure and applied mathematics (John Wiley & Sons : Unnumbered) 606 $aGeometry, Differential 615 0$aGeometry, Differential. 676 $a516.3/63 700 $aAkivis$b M. A$g(Maks Aizikovich)$060194 701 $aGoldberg$b V. V$g(Vladislav Viktorovich)$067439 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910877124903321 996 $aConformal differential geometry and its generalizations$91455464 997 $aUNINA