�ber zweiparametrige ebene Bewegungsvorg�nge

Abstract

TheBlaschke-Grunwald-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.