New representations of Bertrand pairs in Euclidean 3-space

Abstract

In this work, we studied the properties of the spherical indicatrices of a Bertrand curve and its mate curve and presented some characteristic properties in the cases that Bertrand curve and its mate curve are slant helices, spherical indicatrices are slant helices and we also researched that whether the spherical indicatrices made new curve pairs in the means of Mannheim, involute–evolute and Bertrand pairs. Further more, we investigated the relations between the spherical images and introduced new representations of spherical indicatrices.