Initiation to Global Finslerian Geometry

By

  • Hassan Akbar-Zadeh, Doctorat d Etat en Mathématiques Pures June 1961 La Sorbonne, Paris., Director of Research at C.N.R.S., Paris, France.

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.

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Audience

Graduate students, university libraries and researchers.

 

Book information

  • Published: January 2006
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-52106-4


Table of Contents

PrefaceIntroductionI. Linear Connections on a Space of Linear ElementsII. Finslerian ManifoldsIII. Infinitesimal TransformationIV. Geometry of Generalized Einstein ManifoldsV. Properties of Compact Finslerian Manifolds of Non-Negative CurvatureVI. Finslerian Manifolds of Constant Sectional CurvaturesVII. Projective Vector Fields on the Unitary Tangent Fibre BundleVIII. Conformal Vector Fields on the Unitary Tangent Fibre BundleReferences