Family of Surfaces with a Common Special Involute and Evolute Curves

Authors : Süleyman ŞENYURT, Kebire Hilal AYVACI, Davut CANLI

Pages : 160-174

Doi:10.36890/iejg.932757

View : 14 | Download : 5

Publication Date : 2022-04-30

Article Type : Research Paper

Abstract :In this paper, we define the necessary and sufficient conditions for a parametric surface on which both the involute and evolute of any given curve lie to be geodesic, asymptotic and curvature line. Then, the first and second fundamental forms of these surfaces are calculated. By using the Gaussian and mean curvatures, the developability and minimality assumptions are drawn, as well. Moreover we extended the idea to the ruled surfaces. Finally, we provide a set of examples to illustrate the corresponding surfaces.
Keywords : Geodesic curve, involue evolute curves, asymptoticity, curvature line, ruled surfaces