4-dimensional pseudo-Galilean geometry

Abstract

According to F. Klein, Geometry is the study of invariant properties of figures, i.e., properties unchanged under all motions. In this article, we introduce 4-dimensional pseudo-Galilean transformations. Moreover, we study invariant properties under translation, shear and Minkowskian rotation motions. We have computed Frenet-Serret formulas of a curve and also we have found the fundamental theorem of curve theory in 4-dimensional pseudo-Galilean geometry.