In this study, ruled surfaces generated by the tangent, normal, and binormal vectors of the involute curve are investigated. Furthermore, the striction curve of each ruled surface is determined, and the Sannia frame defined along this curve is calculated. Subsequently, the normal vector fields of each surface, the first and second fundamental forms, and the Gaussian and mean curvatures are computed using the coefficients of these fundamental forms. At the end of the study, the developability and minimality of the surfaces are evaluated as results based on their Gaussian and mean curvatures. Additionally, examples of the surfaces are provided, and their graphs are plotted.
Şenyurt, S., Yurttaş, H., Eren, K. (2026). Ruled Surfaces Constructed by the Involute-Evolute Curve with Sannia Frame. Turkish Journal of Mathematics and Computer Science, Volume: 18 Issue: 3. https://doi.org/10.47000/tjmcs.1621463
Bilici, M., Çalışkan, M., Some characterizations for the pair of involute-evolute curves in Euclidean space, Bulletin Of Pure and Applied Sciences, 21E(2002), 289–294.
Eren, K., Yesmakhanova, K., Ersoy, S., Myrzakulov, R., Involute evolute curve family induced by the coupled dispersionless equations, Optik, 270(2022), 169915.
Eren, K., Myrzakulova, Z., Ersoy, S., Myrzakulov, R., Solutions of localized induction equation associated with involute–evolute curve pair, Soft Computing, 28(2024), 105–117.
Ersoy, S., Eren K., Timelike tangent developable surfaces and Bonnet surface, Abstract and Applied Analysis, 2016(2016), 7 pages.
Kelleci, A., Eren, K., On the evolution of some associated type ruled surfaces, Mathematical Sciences and Applications E-Notes, 8(2020), 178–186.
Pressley, A., Elementary Differential Geometry. Second Edition, Springer London Ltd, London UK, 474s, 2010.
Sarıoğlugil, A., Tutar, A., On ruled surfaces in Euclidean space E3, International Journal of Contemporary Mathematical Sciences, 2(2007), 1–11.
Şenyurt, S., Bilici, M., Çalışkan, M., Some characterizations for the involute curves in dual space, International Journal of Mathematical Combinatorics, 1(2015), 113–125.
Şenyurt, S., Eren, K., On ruled surfaces with a Sannia frame in Euclidean 3-space, Kyungpook Mathematical Journal, 62(2022), 509–531.
Şenyurt, S., Ayvacı, H.K., Canlı, D., Some characterizations of spherical indicatrix curves generated by Sannia frame, Konuralp Journal of Mathematics, 9(2021), 222–232.
Sivas, S., Şenyurt, S., Çalışkan, A., Smarandache curves of involute-evolute curve according to Frenet frame, Fundamentals of Contemporary Mathematical Sciences, 4(2023), 31–45.