Initiation to Global Finslerian Geometry - 1st Edition - ISBN: 9780444521064, 9780080461700

Initiation to Global Finslerian Geometry, Volume 68

1st Edition

Authors: Hassan Akbar-Zadeh
Hardcover ISBN: 9780444521064
eBook ISBN: 9780080461700
Imprint: Elsevier Science
Published Date: 18th January 2006
Page Count: 264
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Table of Contents

  • Preface
  • Introduction
  • Chapter I: Linear Connections on a Space of Linear Elements
    • (abstract)
    • I Regular Linear Connections
    • II Curvature and torsion of a regular linear connection
  • Chapter II: Finslerian Manifolds
    • (Abstract)
  • Chapter III: Isometries and Affine Vector Fields on the Unitary Tangent Fibre Bundle
    • Abstract
  • Chapter IV: Geometry Of Generalized Einstein Manifolds
    • (abstract)
    • I Comparison Theorem
    • II Deformation of the Finslerian metric. Generalized Einstein Manifolds
  • Chapter V: Properties of Compact Finslerian Manifolds of Non-negative Curvature
    • (Abstract)
    • II COMPACT FINSLERIAN MANIFOLDS WHOSE INDICATRIX IS AN EINSTEIN MANIFOLD
  • Chapter VI: Finslerian Manifolds of Constant Sectional Curvature [4]
    • (abstract)
    • I Isotropic Finslerian Manifolds
    • III Complete manifolds with constant sectional curvatures
    • IV The Plane Axioms in Finslerian Geometry
  • Chapter VII: Projective Vector Fields on the Unitary Tangent Fibre Bundle [3]
    • (abstract)
  • Chapter VIII: Conformal vector fields on the unitary tangent fibre bundle
    • Abstract
    • 1 The Co-differential of a 2-form.
    • 2 ALemma
    • 3 A Characterisation of Conformal infinitesimal transformations when the manifold is compact
    • 4 Curvature and Infinitesimal Conformal Transformations in the compact case
    • 5 Case when M compact with scalar curvature H˜ constant
    • 6 Case when X = Xi(z) dxi is semi-closed.
  • References
  • Index

Description

  • Preface
  • Introduction
  • Chapter I: Linear Connections on a Space of Linear Elements
    • (abstract)
    • I Regular Linear Connections
    • II Curvature and torsion of a regular linear connection
  • Chapter II: Finslerian Manifolds
    • (Abstract)
  • Chapter III: Isometries and Affine Vector Fields on the Unitary Tangent Fibre Bundle
    • Abstract
  • Chapter IV: Geometry Of Generalized Einstein Manifolds
    • (abstract)
    • I Comparison Theorem
    • II Deformation of the Finslerian metric. Generalized Einstein Manifolds
  • Chapter V: Properties of Compact Finslerian Manifolds of Non-negative Curvature
    • (Abstract)
    • II COMPACT FINSLERIAN MANIFOLDS WHOSE INDICATRIX IS AN EINSTEIN MANIFOLD
  • Chapter VI: Finslerian Manifolds of Constant Sectional Curvature [4]
    • (abstract)
    • I Isotropic Finslerian Manifolds
    • III Complete manifolds with constant sectional curvatures
    • IV The Plane Axioms in Finslerian Geometry
  • Chapter VII: Projective Vector Fields on the Unitary Tangent Fibre Bundle [3]
    • (abstract)
  • Chapter VIII: Conformal vector fields on the unitary tangent fibre bundle
    • Abstract
    • 1 The Co-differential of a 2-form.
    • 2 ALemma
    • 3 A Characterisation of Conformal infinitesimal transformations when the manifold is compact
    • 4 Curvature and Infinitesimal Conformal Transformations in the compact case
    • 5 Case when M compact with scalar curvature H˜ constant
    • 6 Case when X = Xi(z) dxi is semi-closed.
  • References
  • Index

Key Features

  • Theory of connections of vectors and directions on the unitary tangent fibre bundle.
  • Complete list of Bianchi identities for a regular conection of directions.
  • Geometry of generalized Einstein manifolds.
  • Classification of Finslerian manifolds.
  • Affine, isometric, conformal and projective vector fields on the unitary tangent fibre bundle.

Readership

Graduate students, university libraries and researchers.


Details

No. of pages:
264
Language:
English
Copyright:
© Elsevier Science 2006
Published:
Imprint:
Elsevier Science
eBook ISBN:
9780080461700
Hardcover ISBN:
9780444521064

About the Authors

Hassan Akbar-Zadeh Author

Affiliations and Expertise

Director of Research at C.N.R.S., Paris, France.