Canal surfaces in 4-dimensional euclidean space

Abstract

In this paper, we study canal surfaces imbedded in 4-dimensional EuclideanspaceE4. We investigate these surface curvature properties with respect to thevariation of the normal vectors and ellipse of curvature. Some special canalsurface examples are constructed inE4. Furthermore, we obtain necessary andsufficient condition for canal surfaces to become superconformal inE4. At theend, we present the graphs of projections of canal surfaces inE3.

In this paper, we study canal surfaces imbedded in 4-dimensional EuclideanspaceE4. We investigate these surface curvature properties with respect to thevariation of the normal vectors and ellipse of curvature. Some special canalsurface examples are constructed inE4. Furthermore, we obtain necessary andsufficient condition for canal surfaces to become superconformal inE4. At theend, we present the graphs of projections of canal surfaces inE3.