Absolute Parallelism Geometry: Developments, Applications and Problems

Absolute parallelism geometry is frequently used for physical applications. It has two main defects, from the point of view of applications. The first is the identical vanishing of its curvature tensor. The second is that its autoparallel paths do not represent physical trajectories. The present work shows how these defects were treated in the course of development of the geometry. The new version of this geometry contains simultaneous non-vanishing torsion and curvatures. Also, the new paths discovered in this geometry do represent physical trajectories. Advantages and disadvantages of this geometry are given for each stage of its development. Physical applications are just mentioned without giving any details.