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.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Elsevier Science & Technology
Zielgruppe
Für Beruf und Forschung
Graduate students, university libraries and researchers.
Maße
Höhe: 225 mm
Breite: 149 mm
Gewicht
ISBN-13
978-0-444-52106-4 (9780444521064)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Director of Research at C.N.R.S., Paris, France.
Chapter I: Linear Connections on a Space of Linear Elements
Chapter II: Finslerian Manifolds
Chapter III: Isometries and Affine Vector Fields on the Unitary Tangent Fibre Bundle
Chapter IV: Geometry Of Generalized Einstein Manifolds
Chapter V: Properties of Compact Finslerian Manifolds of Non-negative Curvature
Chapter VI: Finslerian Manifolds of Constant Sectional Curvature [4]
Chapter VII: Projective Vector Fields on the Unitary Tangent Fibre Bundle [3]
Chapter VIII: Conformal vector fields on the unitary tangent fibre bundle
References
Index
