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  • Produktbild: Global theory of connections and holonomy groups
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Global theory of connections and holonomy groups

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

13.12.2011

Herausgeber

Andre Lichnerowicz

Verlag

Springer Netherland

Seitenzahl

264

Maße (L/B/H)

24,4/17/1,5 cm

Gewicht

468 g

Auflage

Softcover reprint of the original 1st ed. 1976

Sprache

Englisch

ISBN

978-94-010-1552-3

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

13.12.2011

Herausgeber

Andre Lichnerowicz

Verlag

Springer Netherland

Seitenzahl

264

Maße (L/B/H)

24,4/17/1,5 cm

Gewicht

468 g

Auflage

Softcover reprint of the original 1st ed. 1976

Sprache

Englisch

ISBN

978-94-010-1552-3

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: Global theory of connections and holonomy groups
  • Produktbild: Global theory of connections and holonomy groups
  • I General Notions about Differentiable Manifolds.- 1•1: Differentiable Manifold.- 1•1.1 Atlas: Differentiable Manifold.- .2 Scalar Function Defined on a Manifold.- .3 Mapping of Class C?.- .4 Tangent Vector Spaces at a Point.- . 5 Frames and Coframes.- .6 Pseudoscalars, Orientations, Tensors in a Differentiable Manifold.- .7 The Notion of Differentiable Fibre Bundle.- .8 The Fibre Bundles Attached to a Differentiable Manifold.- .9 Riemannian Manifolds: Whitney’s Theorem.- . 10 Images under a Mapping.- 1•2: Exterior Differential Forms.- 1•2.11 The Kronecker Tensor.- .12 The Space of q-Forms ?x (q).- .13 The Exterior Product.- .14 Exterior Product of Linear q-Forms: Expression for and Value of a q-Form.- .15 Two Results on Exterior Products of Linear Forms.- .16 Reduction of an Exterior Quadratic Form.- .17 Exterior Differential Forms.- .18 Exterior Differential of a q-Form.- .19 Inverse Image of a Form under a Mapping.- 1•2.20 Closed Forms — Local Study.- .21 Pfaffian Systems: Frobenius’ Theorem.- 1•3: Vector Valued Forms.- 1•3.22 Notion of a Vector Valued Form.- .23 Exterior Differential of a Form ?.- .24 Case Where the Vector Space Admits a Lie-Algebraic Structure.- II Infinitesimal Connections: Linear Connections.- 2•1: Homotopy Notions.- 2•1.25 Paths: Homotopy: Poincaré Group.- .26 Factorisation Lemma.- 2•2: Infinitesimal Connections on a Principal Fibre Bundle.- 2•2.27 Principal Fibre Bundle and the Lie Algebra of the Structural Group.- .28 First Definition of an Infinitesimal Connection.- .29 Second Definition of an Infinitesimal Connection.- . 30 Development.- . 31 Local Sections.- .32 Holonomy Groups of an Infinitesimal Connection..- .33 Tensors and Tensor Forms on E.- .34 Passage From One Connection to Another.- .35 Absolute Differential of a q-Form: Curvature of an Infinitesimal Connection.- .36 Expression for the Curvature Form.- 2•3: Linear Connections.- 2•3.37 Notion of Linear Connection.- .38 Explicit Formulae.- .39 The Absolute Differential in a Linear Connection.- .40 Torsion of a Linear Connection.- .41 Curvature of a Linear Connection.- .42 The Bianchi Identities for a Linear Connection.- 2•3.43 Explicit Formulae in Arbitrary Frames and in Local Coordinates.- .44 The Ricci Identity.- .45 Fibre Bundle of Affine Frames.- .46 Affine Connection Associated with a Linear Connection.- .47 Transport Relative to a Linear Connection: Holonomy Groups.- .48 Image of a Linear Connection.- .49 Development on Affine Spaces.- .50 Geodesics.- 2•4: Riemannian Connections.- 2•4.51 Notion of Euclidian Connection: Holonomy Group.- .52 Riemannian Connections.- .53 Properties of the Riemannian Connection.- III Holonomy Groups and Curvature.- 3•1: General Case and Manifolds with a Linear Connection.- 3•1.54 Transport of a Tensor: Tensor with Vanishing Covariant Derivative.- .55 Local Holonomy Group.- .56 Special Local Sections.- .57 Elements of the Lie Algebra of 1.- .58 elements of the lie algebra of 2.- .59 Case of an Infinitesimal Connection on a Principal Fibre Bundle.- .60 Holonomy Group and Curvature.- .61 Case of a Linear Connection.- .62 Notion of Infinitesimal Holonomy Group.- .63 Singular Points for Infinitesimal Holonomy.- .64 Regular Points for Infinitesimal Holonomy.- .65 Points Singular for Local Holonomy.- .66 Connected Components of Holonomy of Vn.- .67 Real Analytic Manifold with an Analytic Connection.- .68 Study of the Group ?x(Vn) in the Case Where ?x(Vn) is Irreducible.- 3•2: Riemannian Manifolds: Reducibility.- 3•2.69 Holonomy Groups.- .70 Reducibility of a Riemannian Manifold.- .71 Complete Reducibility Of ?x.- . 72 Study of the Group ?x.- .73 Study of the Group ?x.- . 74 Geodesic Normal Coordinates.- .75 Complete Riemannian Manifolds: A Theorem by Georges De Rham.- .76 The Group ?x for a Complete Riemannian Manifold.- IV Harmonic Forms and Forms with Zero Covariant Derivative.- 4·1: Elements of Homology.- 4•1.77 Differentiable Chains.- . 78 Boundary.- .79 Integral of a Form: Stokes’ Formula.- .80 Homology on Forms.- 4•2: Harmonic Forms.- 4•2.81 The Volume Element Form on Vn.- .82 The Hodge *-Operator on p-Forms.- .83 The Operators ? and ?.- .84 The Global Scalar Product on a Compact Manifold and Harmonic Forms.- .85 Fundamental Theorems on Harmonic Forms.- 4•3: The Operators Defined by a Form on a Riemannian Manifold.- 4•3.86 Definition of the Operators Kh.- .87 Relations between Kh and Kk-h.- .88 Case Where F has Zero Covariant Derivative: Relations With d and ?.- .89 The Operators Kh and the Operator ?.- .90 Example: Case Where the Degree of F is Twice an Odd Number.- V Almost Complex Manifolds and Subordinate Structures.- 5•1: Complex Structure on a Real Vector Space.- 5•1.91 Complexification of a Real Vector Space.- .92 Complex Structure on a Real Space.- .93 Bases of T2n Adapted to a Complex Structure of T2n.- .94 The Operators C and M on Forms.- 5•2: Hermitian Vector Spaces.- 5•2.95 Notion of Hermitian Vector Space.- .96 Hermitian Structure Subordinate to an Exterior Quadratic Form.- .97 Bases Adapted to a Hermitian Structure.- .98 The Operators L and ? for a Hermitian Vector Space.- .99 Hodge-Lepage Decomposition for a q-Form.- 5•3: Almost Complex Structure and Subordinate Structures on a Differentiable Manifold.- 5•3.100 Manifold with Complex Analytic Structure.- .101 Manifold with Almost Complex Structure.- .102 Torsion of an Almost Complex Structure.- .103 Integrability of an Almost Complex Structure.- .104 Calculation of the Torsion Tensor of an Almost Complex Structure.- .105 Almost Complex Torsion and Vector Fields.- . 106 Almost Hermitian Structure.- 5•4: Almost Complex Connections.- 5•4.107 Complex Linear Connections.- .108 Notion of an Almost Complex Connection.- .109 Real Linear and Almost Complex Connections.- .110 Almost Complex Torsion and Connections.- .111 Almost Hermitian Connections.- .112 Second Canonical Connection of an Almost Hermitian Manifold.- .113 Case of Hermitian and Pseudohermitian Manifolds.- .114 Case of Pseudokählerian Manifolds.- 5•4.115 Quadratic Form with Vanishing Covariant Derivative on A Riemannian Manifold.- .116 Kählerian Manifolds.- .117 Examples of Kählerian Manifolds.- .118 Properties Concerning Holonomy Groups.- .119 Reducibility of Pseudokählerian Manifolds.- 5•5: Forms on Pseudohermitian and Pseudokählerian Manifolds.- 5•5.120 Orthogonality on an Almost Hermitian Manifold.- .121 The Operators d? and d? on an Almost Complex Manifold.- .122 The Operators ?? and ?? on a pseudohermitian Manifold.- .123 On the Operators M, d and ? on a Pseudohermitian Manifold.- .124 Operators on a Pseudokählerian Manifold.- .125 Global Properties of Compact Pseudokählerian Manifolds.- List of Symbols.