Fermi-Walker Parallel Transport According to Quasi Frame in Three Dimensional Minkowski Space

Abstract

A relativistic observer ξ needs reference frames in order to measure the movement and position of a object. If ξ is free falling, its restspaces are transported with LeviCivita parallelism. For accelerated observes, the restspaces are not transported by the Levi-Civita parallelism. In this case Fermi-Walker parallelism is used to define constant directions. Fermi-Walker parallelism is an isometry between the tangent spaces along relativistic observer ξ. [6, 11]. Balakrishnan et al investigated time evolutions of the space curve associated with a geometric phase using Fermi-Walker parallel transport in three dimensional Euclidean space [2]. Gürbüz had introduced new geometric phases according three classes of a curve evolution in Minkowski space [7, 8]. Usual Fermi-Walker parallel derivative for any vector field A is given with respect to Frenet frame {t, n, b} in three dimensional Euclidean space as following (cf. [9]) DfA Dfs = dA