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.