Theory of multicodimensional (n + 1)-webs

摘要: 1 Differential Geometry of Multicodimensional (n + 1)-Webs.- 1.1 Fibrations, Foliations, and d-Webs W(d, n, r) Codimension r on a Differentiable Manifold Xnr.- 1.1.1 Definitions Examples.- 1.1.2 Closed Form Equations Web W(n 1, Further 1.2 The Structure Fundamental Tensors r).- 1.2.1 Moving Frames Associated with 1.2.2 1.2.3 W(3, 2, 1.2.4 Special Classes 3-Webs 1.3 Invariant Affine Connections 1.3.1 Geometrical Meaning the Forms Wji(?).- 1.3.2 an 1)-Web.- 1.3.3 Induced by Connnection ?n+ Leaves.- 1.3.4 3-Subwebs 1.4 Webs Vanishing Curvature.- 1.5 Parallelisable 1.6 1)-Webs Paratactical 3-Subwebs.- 1.7 Integrable Diagonal Distributions 4-Subwebs.- 1.8 Distributions.- 1.9 Transversally Geodesic 1.10 Hexagonal 1.11 Isoclinic Notes.- 2 Almost Grassmann Structures 2.1 Manifold.- 2.1.1 Segre Variety Cone.- 2.1.2 Structures.- 2.2 Torsion Tensor 2.3 An 2.4 Semiintegrable 2.5 Double Webs.- 2.6 Problems Grassmannisation Algebraisation Their Solution for r), d ? n 1.- 2.6.1 Problem l, 2.6.2 d> 2.6.3 2.6.4 2.6.5 3 Local n-Quasigroups 3.1 3.2 Its Coordinate in Neighbourhood Point.- 3.3 Computation Components Curvature Terms Equations.- 3.4 Relations between Alternators Parastrophic n-Quasigroups.- 3.5 Canonical Expansions Analytic n-Quasigroup.- 3.6 One-Parameter n-Subquasigroups 3.7 Comtrans Algebras.- 3.7.1 Preliminaries.- 3.7.2 3.7.3 Masking.- 3.7.4 Lie's Third Theorem 3-Loops.- 3.7.5 General Case n-Loops.- 4 4.1 Reducible 4.2 Multiple Completely 4.3 Group 4.4 (2n 2)-Hedral 4.5 Bol 4.5.1 Definition Properties Moufang 4.5.2 Closure Conditions.- 4.5.3 A Geometric Characteristic 4.5.4 Condition (Bn 1n 1).- 5 Realisations 5.1 5.1.1 Basic Definitions.- 5.1.2 Projective Space.- 5.1.3 Specialisation Frames.- 5.1.4 5.1.5 Surfaces 5.1.6 Hexagonality 1)-Web 2nd U?.- 5.2 5.3 5.4 Algebraic, Algebraic 5.4.1 5.4.2 5.4.3 5.4.4 5.4.5 Four-Webs.- 5.4.6 5.5 5.6 5.7 4-Web Formed Four Pencils (2r)-Planes P3r.- 5.8 4-Webs 6 Applications Theory 6.1 Application to Point Correspondences Lines.- 6.1.1 6.1.2 among Lines One-Codimensional 6.1.3 Correpondences.- 6.1.4 Correspondences.- 6.1.5 Godeaux Homography.- 6.1.6 Homographies.- 6.2 Spaces.- 6.2.1 6.2.2 6.2.3 6.2.4 6.2.5 6.2.6 6.3 Holomorphic Mappings Polyhedral Domains.- 6.3.1 Introductory Note.- 6.3.2 Analytical Domains Cn, n> 6.3.3 Meromorphic 6.3.4 Partition Generated 6.3.5 Foliations.- 6.3.6 Functions.- 7 Four-Webs W(4, 7.1 geometry 7.1.1 Notions 7.1.2 Basis Affinor.- 7.1.3 Transversal Bivectors 4-Web.- 7.1.4 Permutability Transformations [?, ?].- 7.1.5 7.1.6 7.1.7 Conditions Geodesicity Some Leaves Connection ?123.- 7.2 7.2.1 7.2.2 7.2.3 7.2.4 (Continuation).- 7.2.5 3-Subweb.- 7.3 Pair Orthogonal Quasigroups 7.3.1 7.3.2 B.- 7.4 Satisfying Desargues Triangle 7.4.1 D1.- 7.4.2 Two Conditions, D1 D2.- 7.4.3 D12.- 7.4.4 7.4.5 7.5 Classification 3).- 7.6 GW(4, 7.6.1 Notions.- 7.6.2 7.6.3 Equations, Tensors, Affinor 7.6.4 7.7 7.8 AW(4, 8 Rank 8.1 Grassmannisable Algebraisable 8.1.1 3.- 8.1.2 AGW(d,2,r), > 8.1.3 AGW(d, 8.1.4 AAW(d, 8.1.5 Non-Isoclinic AGW(4, 2).- 8.1.6 Examples Non-Extendable 8.2 1-Rank 8.2.1 Non-Zero 1-Rank.- 8.2.2 Upper Bound 8.2.3 Description 4,r Maximum 8.2.4 Explicit Expressions Functions ?? Level Sets.- 8.3 r-Rank 8.3.1 8.3.2 2) 2-Rank.- 8.3.3 2), 4, 8.3.4 8.4 8.4.1 Case.- 8.4.2 8.5 Exceptional 8.5.1 Fibrations 8.5.2 Interior Products Four-Web.- 8.5.3 Exterior 3-Forms 8.5.4 Infinitesimal Automorphisms Cubic 8.5.5 Conformai Symbols Frequently Used.