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 2 1 (r). In this paper, we reconsider the canal surfaces for all Lorentz spheres which are pseudo sphere S 2 1 (r), pseudo-hyperbolic sphere H 2 (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 2 0 (r) and the singular points of the spacelike tubular surface obtained from pseudo-hyperbolic sphere H 2 0 (r). Mathematics Subject Classification. 53B30, 53C50, 53A35.

Canal Surface Whose Center Curve is a Hyperbolic Curve with Hyperbolic Frame

“…In [5], [6], [7], [8], the authors study canal surfaces and tubular surfaces in Euclidean 3-space, Minkowski 3-space, Galilean and Pseudo Galilean spaces. Lately, in [13], the authors consider the new approach to canal surfaces. Also in [2] and [9], the authors study canal surfaces with quaternions.…”

Identifying Canal Surfaces in E4 : Characterization of a Special Case

“…Canal surfaces have extensive applications in computer aided geometric design [1,2]. There are many studies in the literature, related to canal and tube surfaces [3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Geometric Characterizations of Canal Surfaces in Minkowski 3-Space II

“…spacelike curve, timelike curve, or null curve). The classification of canal surfaces was obtained by Ucum and Ilarslan in [6]. For convenience, the authors of this paper denoted the notations for all kinds of canal surfaces in E 3 1 .…”