Canal surfaces in 4-dimensional Euclidean space

Abstract

In the present study, we consider canal surfaces imbedded in an Euclidean space of four dimensions. The curvature properties of these surface are investigated with respect to the variation of the normal vectors and curvature ellipse. We also give some special examples of canal surfaces in E^4. Further, we give necessary and sufficient condition for canal surfaces in E^4 to become superconformal. Finally, the visualization of the projections of canal surfaces in E^3 are presented.

Identifying Canal Surfaces in E4 : Characterization of a Special Case

“…In [21], the geometric properties of these type of surfaces are examined. Also, equivalent parametrization is studied with respect to the Bishop frame in Proof: As in the proof of Theorem 3.1, the following equations can be written: An easy computation shows that:…”

“…where   12 ( ), ( ), ( ), ( ) T u N u B u B u is the Frenet frame of () u  . The investigation of the curvature properties of these surfaces are examined in [21]. Also in [22], loxodromes on tube surface with variable radii u are studied.…”

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

“…In [18] and [19], some features of offset curves are discussed thoroughly. 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 .…”

A new type of canal surface in Euclidean 4-space E^4

“…In [1-5, 8, 10, 12, 15, 19, 25], authors give some characteristic properties of surfaces in 4 IE . Furthermore, in [9,17] authors consider canal surfaces in 4 IE .…”