An Ap-Structure with Finslerian Flavor: I

Abstract

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.

13 pages, LaTeX file, typographical corrections. Part of a talk presented at The International Conference on "Finsler Extensions of Relativity Theory" held at Cairo, Egypt, November 4-10,2006

References in corpus (4)

• Cosmological Results from High-z Supernovae
• Rotation Curves of Spiral Galaxies
• Alternatives to Dark Matter and Dark Energy
• Linear Connections and Curvature Tensors in the Geometry of Parallelizable Manifolds

Cited by in corpus (7)

• Bounce inflation in $f(T)$ Cosmology: A unified inflaton-quintessence field
• The Hidden Flat Like Universe: Starobinsky-like inflation induced by f(T) gravity
• Reconstruction of $f(T)$-gravity in the absence of matter
• Teleparallel Lagrange Geometry and a Unified Field Theory
• The Hidden Flat Like Universe II: Quasi inverse power law inflation by $f(T)$ gravity
• An AP-Structure with Finslerian Flavor: Path Equations
• On Finslerized Absolute Parallelism spaces