| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910877124903321 |
|
|
Autore |
Akivis M. A (Maks Aizikovich) |
|
|
Titolo |
Conformal differential geometry and its generalizations / / Maks A. Akivis, Vladislav V. Goldberg |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
|
|
|
|
ISBN |
|
1-283-28111-2 |
9786613281111 |
1-118-03263-2 |
1-118-03088-5 |
|
|
|
|
|
|
|
|
Descrizione fisica |
|
1 online resource (404 p.) |
|
|
|
|
|
|
Collana |
|
Pure and applied mathematics |
|
|
|
|
|
|
Altri autori (Persone) |
|
GoldbergV. V (Vladislav Viktorovich) |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
"A Wiley-Interscience publication." |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references (p. 323-354) and indexes. |
|
|
|
|
|
|
Nota di contenuto |
|
Conformal 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 |
CHAPTER 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 |
NotesCHAPTER 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 |
6.2 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 |
7.5 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 |
|
|
|
|
|
|
Sommario/riassunto |
|
Comprehensive 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 |
|
|
|
|
|
|
|
| |