On some 1,3H3 - helicoidal surfaces and their parallel surfaces at a certain distance in 3 - dimensional Minkowski space

Abstract

The surface obtained by rotating a curve from the plane (ξ₁ ξ ₃) around the space- like axis ξ ₃, where ξ₁ = (1; 0; 0) and ξ ₃ = (0; 0; 1), and simultaneously translating it along that axis is called ^1,3H₃ - helicoidal surface. Let S and S be two surfaces and let δ be a constant positive real number. S and S are parallel at distance δ if for each point P  S we have P (u; v) = P(u; v) + δ n(u; v), where n is the unit normal vector field on S. In this paper we find some properties of some linear ^1,3H₃ - helicoidal surfaces and of their parallel surfaces in 3 - dimensional Minkowski space R₁³.