An Ap-Structure with Finslerian Flavor: I

Understand

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.