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

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 $γ$ 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.

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