TY  - JOUR
T1  - Family of Surfaces with a Common Special Involute and Evolute Curves
AU  - Şenyurt, Süleyman
AU  - Ayvacı, Kebire Hilal
AU  - Canlı, Davut
PY  - 2022
DA  - April
Y2  - 2021
DO  - 10.36890/iejg.932757
JF  - International Electronic Journal of Geometry
JO  - Int. Electron. J. Geom.
PB  - Kazım İlarslan
WT  - DergiPark
SN  - 1307-5624
SP  - 160
EP  - 174
VL  - 15
IS  - 1
LA  - en
AB  - 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.
KW  - Geodesic curve
KW  - involue-evolute curves
KW  - asymptoticity
KW  - curvature line
KW  - ruled surfaces.
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UR  - https://doi.org/10.36890/iejg.932757
L1  - https://dergipark.org.tr/en/download/article-file/1751211
ER  -