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Shelekhov / Akivis

Geometry and Algebra of Multidimensional Three-Webs

Medium: Buch
ISBN: 978-0-7923-1684-8
Verlag: Springer Netherlands
Erscheinungstermin: 31.03.1992
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·Et moi,., Ii j'avait so comment en revenir. je One serviee mathematics has rendered the n 'y serais point all~.' human nee. It hal put rommon sense back Jules Verne whme it belongs, on the topmost shelf next to the dusty canister labelled' discarded nonsense'. The series il divergent; therefore we may be EricT. Bell able to do scmething with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlineari­ ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci­ ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser­ vice topology has rendered mathematical physics. '; 'One service logic has rendered computer science.'; 'One service category theory has rendered mathematics.'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Produkteigenschaften

  • Artikelnummer: 9780792316848
  • Medium: Buch
  • ISBN: 978-0-7923-1684-8
  • Verlag: Springer Netherlands
  • Erscheinungstermin: 31.03.1992
  • Sprache(n): Englisch
  • Auflage: 1992
  • Serie: Mathematics and its Applications
  • Produktform: Gebunden
  • Gewicht: 735 g
  • Seiten: 358
  • Format (B x H x T): 160 x 241 x 25 mm
  • Ausgabetyp: Kein, Unbekannt

Themen

Autoren/Hrsg.

Autoren

1 Three-Webs and Geometric Structures Associated with Them.- 1.1 G-Structures, Fibrations and Foliations.- 1.2 Three-Webs on Smooth Manifolds.- 1.3 Geometry of the Tangent Space of a Multidimensional Three-Web.- 1.4 Structure Equations of a Multidimensional Three-Web.- 1.5 Parallelizable and Group Three-Webs.- 1.6 Computation of the Torsion and Curvature Tensors of a Three-Web.- 1.7 The Canonical Chern Connection on a Three-Web.- 1.8 Other Connections Associated with a Three-Web.- 1.9 Subwebs of Multidimensional Three-Webs.- Problems.- Notes.- 2 Algebraic Structures Associated with Three-Webs.- 2.1 Quasigroups and Loops.- 2.2 Configurations in Abstract Three-Webs.- 2.3 Identities in Coordinate Loops and Closure Conditions.- 2.4 Local Differentiable Loops and Their Tangent Algebras.- 2.5 Tangent Algebras of a Multidimensional Three-Web.- 2.6 Canonical Coordinates in a Local Analytic Loop.- 2.7 Algebraic Properties of the Chern Connection.- Problems.- Notes.- 3 Transversally Geodesic and Isoclinic Three-Webs.- 3.1 Transversally Geodesic and Hexagonal Three-Webs.- 3.2 Isoclinic Three-Webs.- 3.3 Grassmann Three-Webs.- 3.4 An Almost Grassmann Structure Associated with a Three-Web. Problems of Grassmannization and Algebraization.- 3.5 Isoclinicly Geodesic Three-Webs. Three-Webs over Algebra.- Problems.- Notes.- 4 The Bol Three-Webs and the Moufang Three-Webs.- 4.1 The Bol Three-Webs.- 4.2 The Isoclinic Bol Three-Webs.- 4.3 The Six-Dimensional Bol Three-Webs.- 4.4 The Moufang Three-Webs.- 4.5 The Moufang Three-Web of Minimal Dimension.- Problems.- Notes.- 5 Closed G-Structures Associated with Three-Webs.- 5.1 Closed G-Structures on a Smooth Manifold.- 5.2 Closed G-Structures Defined by Multidimensional Three-Webs.- 5.3 Four-dimensional Hexagonal Three-Webs.- 5.4 The Closure ofThe G-Structure Defined by a Multidimensional Hexagonal Three-Web.- 5.5 Three-Webs and Identities in Loops.- Problems.- Notes.- 6 Automorphisms of Three-Webs.- 6.1 The Autotopies of Quasigroups and Three-Webs.- 6.2 Infinitesimal Automorphisms of Three-Webs.- 6.3 Regular Infinitesimal Automorphisms of Three-Webs.- 6.4 G-Webs.- Problems.- Notes.- 7 Geometry of the Fourth Order Differential Neighborhood of a Multidimensional Three-Web.- 7.1 Computation of Covariant Derivatives of the Curvature Tensor of a Three-Web.- 7.2 Internal Mappings in Coordinate Loops of a Three-Web.- 7.3 An Algebraic Characterization of the Tangent W4-Algebra of a Three-Web.- 7.4 Classification of Three-Webs in the Fourth Order Differential Neighborhood.- 7.5 Three-Webs with Elastic Coordinate Loop.- Problems.- Notes.- 8 d-Webs of Codimension r.- 8.1 (n + 1)-Webs on a Manifold of Dimension nr.- 8.2 (n + 1)-Webs on a Grassmann Manifold.- 8.3 (n + 1)-Webs and Almost Grassmann Structures.- 8.4 Transversally Geodesic and Isoclinic (n + 1)-Webs.- 8.5 d-Webs on a Manifold of Dimension nr.- 8.6 The Algebraization Problem for Multidimensional d-Webs.- 8.7 The Rank Problem for d-Webs.- Problems.- Notes.- Appendix A.- Symbols Frequently Used.