A new approach to canal surface with parallel transport frame

Abstract

In the present study, we attend to the canal surfaces with the spine curve [Formula: see text] according to the parallel transport frame in Euclidean [Formula: see text]-space [Formula: see text]. We give an example of these surfaces and obtain some results about curvature conditions in [Formula: see text]. Moreover, the visualizations of projections of canal surfaces are presented. Lastly, we give the necessary and sufficient conditions for canal surfaces to become weak superconformal.

Tubular Surface Having Pointwise 1-type Gauss Map in Euclidean 4-Space

“…In [8], authors consider canal surfaces in E 4 . Also in [24,25], the authors studied canal surfaces with parallel transport frame in E 4 .…”

On Bishop frame of a pseudo null curve in Minkowski space-time

“…In Minkowski space-time E 4 1 the Bishop frame {T 1 , N 1 , N 2 , N 3 } of a null Cartan curve contains the tangent vector field T 1 of the curve and three vector fields whose derivatives N ′ 1 , N ′ 2 , and N ′ 3 with respect to pseudo-arc are collinear with N 2 [7]. Hence, they make a minimal rotations in the corresponding spaces [6], computer graphics [23], deformation of tubes [21], sweep surface modeling [16], and differential geometry in studying different types of curves (see for example [2,3,15,24]).…”

“…Accordingly, the Bishop frame of null Cartan curve in E 4 1 can be seen as rotation-minimizing frame with respect to N 2 . The Bishop frame can be used in many physical and mathematical applications related with rigid body mechanics [6], computer graphics [23], deformation of tubes [21], sweep surface modeling [16], and differential geometry in studying different types of curves (see for example [2,3,15,24]).…”

Spacelike Translation Surfaces in Minkowski 4-Space E_1^4

“…During 1960s, the pioneering work of Osserman influenced the majority of modern theories of minimal surfaces in three dimensional spaces [17]. Minimal surfaces have also been the subject of today's work (see, [16]).…”