Abstract
In this paper, the curves associated with the Combescure transform are discussed. With the help of the fact that these curves have a common Frenet frame, an equivalence relation is defined. The equivalence classes obtained by this equivalence relation have been examined for some special curves and it has been obtained that all curves in the equivalence class of a helix curve are also helix curves. This is also true for k-slant helix curves. The important part of this paper consists of the useful construction method to obtain a curve from the given curve α with the help of Combescure transformation. With this method, some special curves such as Bertrand, Mannheim, Salkowski, anti-Salkowski or spherical curve can be obtained from any curve related by a Combescure transform. For example, we obtain an example of Mannheim curves explicitly obtained from an anti-Salkowski curve. It is not easy to find an example of Mannheim curves except circular helix in the literature. In general, the condition for being Bertrand anti-Salkowski or spherical curve of the curve β obtained from the given curve α with the help of Combescure transformation were obtained.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Dynamical Systems and Geometric Theories
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
