On a geometry with torsion and curvature: Basic geometric structure

Abstract

In this paper, we developed, in detail, the geometric structure of a certain type of geometry usually used in physical applications. This paper contains building blocks (BB), tensors of different orders, curves admitted by the geometry and a comparison between this geometry and others used in the literature. Second-order symmetric and skew-symmetric tensors, usually used for physical applications in the context of the geometrization philosophy, are given. Also, in the framework of the same philosophy, the admitted curves can be used as equations of motion of test particles for any field theory constructed in this geometry.