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Youssef, Nabil L.; Sid-Ahmed, Amr M.; Taha, Ebtsam H.

On Finslerized absolute parallelism spaces. (English) Zbl 1275.53029

Int. J. Geom. Methods Mod. Phys. 10, No. 7, Article ID 1350029, 21 p. (2013).
The present paper studies Finsler geometry from the point of view of parallelizable manifolds. The main notion is that of Finsler parallelizable space (FP-space). The geometry of absolute parallelism admits at least four linear connections, two of them are non-symmetric and three of which have non-vanishing curvature tensor. The aim of the authors is to consider FP-spaces as better candidates for the attempts of unification of fundamental interactions, and then some special FP-spaces are considered: Landsberg, Berwald, Minkowskian and Riemannian.
Reviewer: Radu Miron (Iaşi)

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
53B50 Applications of local differential geometry to the sciences
51P05 Classical or axiomatic geometry and physics

Keywords:

pullback bundle; nonlinear connection; Finsler space; generalized absolute parallelism space; generalized Lagrange space; Landsberg space; Berwald space; Minkowskian space; Riemannian space
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References:

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