A new characterization of canal surfaces with parallel transport frame in Euclidean space ${\mathbb{E}}^4$

Abstract

In this study, we consider canal surfaces according to parallel transport frame in Euclidean space ${\mathbb{E}}^4$. The curvature properties of these surfaces are investigated with respect to $k_1$, $k_2$ and $k_3$ which are principal curvature functions according to parallel transport frame. We also give an example of canal surfaces in ${\mathbb{E}}^4.$ Further, we point out that if spine curve $\gamma$ is a straight line, then $M$ is a Weingarten canal surface and also $M$ is a linear Weingarten tube surface. Finally, the visualization of the projections of canal surfaces in ${\mathbb{E}}^3$ are shown.

Cited by in corpus (1)

• Some Characterizations of Focal Surfaces of A Tubular Surface in E^3