Cylinder-like Pappus's hexagon theorem in Nil geometry

Abstract

In this paper we deal with Nil geometry, in whose projective model the geodesic curves are helix-like and fit onto geodesic Nil cylinders of revolution with fibrum axes. In this paper we investigate relations for geodesic cylinders and thus also geodesic curves, which lead to an analogous result to Pappus's hexagon theorem and provide important information about the structure of the considered space.

16 pages, 3 figures