### 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 (*ξ*_{1}* ξ* _{3}) around the space- like axis *ξ* _{3}, where *ξ*_{1} = (1*; *0*; *0) and *ξ* _{3} = (0*; *0*; *1), and simultaneously translating it along that axis is called ^{1,3}*H*_{3} - 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 ^{1,3}*H*_{3} - helicoidal surfaces and of their parallel surfaces in 3 - dimensional Minkowski space R_{1}^{3}.