Family of Surfaces with a Common Special Involute and Evolute Curves

Yıl 2022, Cilt: 15 Sayı: 1, 160 - 174, 30.04.2022

Süleyman Şenyurt , Kebire Hilal Ayvacı , Davut Canlı

https://doi.org/10.36890/iejg.932757

Cited By: 1

Öz

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.

Anahtar Kelimeler

Geodesic curve, involue-evolute curves, asymptoticity, curvature line, ruled surfaces.

Proje Numarası

yok

Kaynakça

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