Time-Like Sweeping Surfaces with a Bishop Frame in the Minkowski 3-Space ${\mathbb{E}}_1^3$

Abstract

In this paper, we consider a time-like sweeping surface and its local singularities with Bishop frame in Minkowski 3-space E 1 3 . Subsequently, we derive the sufficient and necessary conditions for this surface to be spacelike developable ruled surface. In particular, we mainly focus on the study for the resulting spacelike developable surface is a cylinder, cone or tangent surface. Finally, some representative curves are chosen to construct the corresponding spacelike developable surfaces.

Investigation on Isotropic Bezier Sweeping Surface "IBSS" with Bishop Frame

“…Surfaces having no Gaussian curvature could be developable. If and only if the mean curvature vanishes identically, a surface ℳ ⊂ ℝ 3 counts as minimal [11], [2], [3].…”

“…Theorem 3.1. 3 The isotropic Bezier sweeping surface given by ( 22) is Weingarten surface if 𝑘𝑘 2 (𝑑𝑑) = 0 Proof:-Weingarten by differential Eq. ( 23),( 24) Then the isotropic Bezier sweeping surface is the Weingarten surface.…”

“…The Frenet frame can be used to parameterize the sweeping surface. However, it has no definitions at inflection points or along straight curve stretches when the curvature disappears [3], [4].…”

“…In this study, we are able to derive new linked surfaces by employing the Bishop frame in isotropic space 𝐸𝐸 3 1 , we will study an Isotropic Bezier sweeping surface's characteristics.…”