Bertrand and Mannheim Curves of Spherical Framed Curves in a Three-Dimensional Sphere

Abstract

We investigated differential geometries of Bertrand curves and Mannheim curves in a three-dimensional sphere. We clarify the conditions for regular spherical curves to become Bertrand and Mannheim curves. Then, we concentrate on Bertrand and Mannheim curves of singular spherical curves. As singular spherical curves, we considered spherical framed curves. We define Bertrand and Mannheim curves of spherical framed curves. We give conditions for spherical framed curves to become Bertrand and Mannheim curves.

Preface to: Differential Geometry: Structures on Manifolds and Their Applications

“…One can distinguish several topics that have been investigated in the papers of this Special Issue. In addition to the proposed keywords we have already presented in the beginning, we also have some specific ones that appeared in the papers [1][2][3][4][5][6][7][8][9][10][11] that we emphasize in Table 2.…”