Invariants of points in the two dimensional lorentzian similarity geometry

In this thesis, the generalized linear pseudo-similarity groups, the generalized pseudosimilarity motion groups and pseudo-similarity motion groups in two-dimensional Lorentzian similarity geometry are introduced. Relations between the elements of these groups and hyperbolic numbers are given. Invariants of 𝑚-points in two dimensional Lorentzian similarity geometry are found for these groups. The equivalence (or pseudosimilarity) conditions of the two systems consisting of 𝑚-points for these groups are given in terms of the invariants of these points. Moreover, for the given two systems consisting of 𝑚-points satisfying the equivalence conditions, the evident forms of pseudo-similarity transformations are obtained in the terms of common invariants of these systems. Key Words: Invariant, pseudo-similarity transformations, hyperbolic numbers, Lorentzian similarity geometry