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Initiation to Global Finslerian Geometry

  • 1st Edition, Volume 68 - January 18, 2006
  • Latest edition
  • Author: Hassan Akbar-Zadeh
  • Language: English

After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment… Read more

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Description

After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, projective and conformal vector fields on the unitary tangent fibre bundle.



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.

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.

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

Product details

  • Edition: 1
  • Latest edition
  • Volume: 68
  • Published: January 18, 2006
  • Language: English

About the author

HA

Hassan Akbar-Zadeh

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

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