�ber die Leitfl�chen konstanten Mittenabstandes von Geradenkongruenzen des einfach isotropen Raumes

Abstract

In the simply isotropic space J3(1) let S be a congruence of straight lines with the unit vector giving the direction of its lines\(\vec e\)(u,v) and with middle surface\(\vec p\)(u,v). A surface of reference\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {p} _t (u,v): = \vec p(u,v) + t(u,v) \vec e(u,v)\) has constant distance from\(\vec p\)(u,v) if t= const. In this paper we first investigate the mapping, which is established by the lines of S between two arbitrary surfaces of the above type. Next we give a new characterization of the focal points of some hyperbolic lines of the congruence S. Finally, we study some associated ruled surfaces of S, which are connected to the surfaces\(\vec p_t\)(u,v), t ∈ ℝ.