Über zweiparametrige ebene Bewegungsvorgänge

Abstract

TheBlaschke-Grünwald-map associates to each surface β in the quasielliptic space a planar euclidean two-parameter motion$\mathfrak{B}$. Using this map we find kinematic meanings of the Gaussian quasielliptic curvature and furthermore some theorems about the asymptotic motions of$\mathfrak{B}$. The kinematic equivalent of the relation of left-conjugated tangents in points of β is a regular or singular projectivity σ on each poleline of$\mathfrak{B}$. This projectivities have been studied already byH. J. E. Beth andW. v.d. Woude. We show that in every position the quadratic curvature transformations of almost all one-parameter motions of$\mathfrak{B}$ are determined by σ.