Generic properties of helices and Bertrand curves

Abstract

We study generic properties of cylindrical helices and Bertrand curves as applications of singularity theory for plane curves and spherical curves. (2000): 58C27, 53A25, 53A05. Mathematics Subject Classification

A note on Bertrand curves of constant precession

“…Izumiya and Takeuchi [1] studied helices and Bertrand curves. In [2] the authors gave characterizations for Bertrand curves in n dimensional Lorentz space and obtained some results on this space.…”

Bertrand and Mannheim partner -curves on parallel surfaces

“…The well-known examples of such curves are Bertrand curves, involute-evolute curves and Mannheim curves which are studied by many mathematicians in different spaces [2,3,4,5,10,12,14,16]. Moreover, some new definitions of special curve pairs have been given by Kazaz and et al They have considered the notions of Bertrand curve and Mannheim curve for the curves lying fully on regular surfaces and called these curve pairs as Bertrand partner D-curves and Mannheim partner D-curves.…”

Associated Curves of Frenet curves in Three Dimensional Compact Lie Group

“…[1,11,13,20,23] and these special curves, especially helices, are used in many applications [2,9,10,19]. Similarly, by considering two curves, some special curve pairs such as involute-evolute curves, Bertrand curves, Mannheim curves have been defined and studied so far [4,12,14,15,18,21,22].…”