An Ap-Structure with Finslerian Flavor: I

Details An Ap-Structure with Finslerian Flavor: I An Ap-Structure with Finslerian Flavor: I

2008-01-07

arxiv.org/abs/0801.1132v2

Mod.Phys.Lett.A24:1749-1762,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, LaTeX file, typographical corrections. Part of a talk presented at The International Conference on "Finsler Extensio

Scientific paper

10.1142/S0217732309030412

A geometric structure (FAP-structure), having both absolute parallelism and Finsler properties, is constructed. The building blocks of this structures are assumed to be functions of position and direction. A non-linear connection emerges naturally and is defined in terms of the building blocks of the structure. Two linear connections, one of Berwald type and the other of the Cartan type, are defined using the non-linear connection of the FAP. Both linear connections are non-symmetric and consequently admit torsion. A metric tensor is defined in terms of the building blocks of the structure. The condition for this metric to be a Finslerian one is obtained. Also, the condition for an FAP-space to be an AP-one is given.

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