Canal hypersurfaces according to one of the extended Darboux frame field in Euclidean 4-space

Abstract

In the present study, we deal with canal hypersurfaces according to extended Darboux frame field of second kind in Euclidean 4-space (E4) and in this context, firstly we obtain the Gaussian, mean and principal curvatures of the canal hypersurface according to extended Darboux frame field of second kind and give some results for flatness and minimality of these hypersurfaces in E4. Also, we give some results for Weingarten canal hypersurfaces according to extended Darboux frame field of second kind in E4 and finally, we construct an example.