Verallgemeinerung des Wendekreises der Ebenen Euklidischen Kinematik auf Cayley/Klein-Zwangläufe 1. Art

In 12] the local kinematics of all seven Cayley/Klein-planes (CK-planes) was developed in a largely uniform way. The motions of Euclidean, pseudo-Euclidean, elliptic and hyperbolic planes were called CK-motions of 1^st kind. They are fundamentally different from quasielliptic, quasihyperbolic and isotropic motions (CK motions of 2^nd kind). In this paper we consider a uniform generalization of the inflection circle of plane Euclidean kinematics to CK-motions of 1^st kind, which turns out to be a curve of 2^nd order. It can be shown that many important properties of the Euclidean inflection circle are retained. We also generalize the Euclidean cuspidal circle, inflection point and cuspidal point.

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Herrn Prof. Dr.Oswald Giering zum 60. Geburtstag gewidmet