New Types of Canal Surfaces in Minkowski 3-Space

Abstract

Canal surface is a surface formed as the envelope of a family of spheres whose centers lie on a space curve. In Minkowski 3-space, many authors studied canal surfaces. However, when one investigates the papers, it is obvious that the parametrizations of the canal surfaces were found with respect to only pseudo sphere \({S_{1}^{2}(r)}\). In this paper, we reconsider the canal surfaces for all Lorentz spheres which are pseudo sphere \({ S_{1}^{2}(r)}\), pseudo-hyperbolic sphere H2(r) or lightlike cone C and we find the parametrizations of the surfaces. Moreover, we found the parametrization of the tubular surfaces with respect to all Lorentz spheres. Also, we study Weingarten and linear Weingarten type spacelike tubular surface obtained from pseudo-hyperbolic sphere \({H_{0}^{2}(r)}\) and the singular points of the spacelike tubular surface obtained from pseudo-hyperbolic sphere \({H_{0}^{2}(r)}\).