On the Geometry of Finslerized Parallelizable Manifolds

In this work we introduce and investigate a new kind of geometry which we refer to as a “Finslerized Parallelizable geometry”(FP-geometry). We construct a Finsler structure within the framework of a Generalized Absolute Parallelism space (GAP-space). The Finsler structure is obtained from the vector fields forming the parallelization of the GAP-space. The resulting space combines within its geometric structure the simplicity of GAP-geometry and the richness of Finsler geometry hence is potentially more suitable for applications and especially for describing physical phenomena. A study of the geometry of the two structures and their interrelation is carried out. Some special FP-spaces are singled out. One physical application is introduced using that frame.