A Study on Normal Motion of the Torus of Revolution in ℝ³

[1] Leung, C. (2011), Mean Curvature Flow in Euclidean spaces, Lagrangian Mean Curvature Flow, and Conormal Bundles, Master thesis, University of Waterloo, Ontario, Canada. Search in Google Scholar

[2] Yoon, D.W., Yuzbasi, Z.K., Aslan, E.C. (2022), Evolution of space-like curves and special time-like ruled surfaces in the Minkowski space, Indian Journal of Physics, 96, 995-999. Search in Google Scholar

[3] Kaymanli, G.U., Ekici, C., Dede, M. (2020), Directional Evolution of the Ruled Surfaces via the Evolution of Their Directrix Using q-frame along a Time-like Space Curve, EJOSAT, 20, 392-396. Search in Google Scholar

[4] Abd Ellah, H. (2015), Evolution of translation surfaces in Euclidean 3-space E³, Applied Mathematics and Information Sciences, 9, 661-668. Search in Google Scholar

[5] Nakayama, K., Wadati, M. (1993), The Motion of Surfaces, Journal of the Physical Society of Japan, 62, 1895-1901. Search in Google Scholar

[6] Smoczyk, K. (2000), Remarks on the Inverse Mean Curvature Flow, ASIAN J. MATH., 4, 331-336. Search in Google Scholar

[7] Eren, K., Kosal, H. H. (2020), Evolution of space curves and the special ruled surfaces with a modified orthogonal frame, AIMS Mathematics, 5, 2027-2039. Search in Google Scholar

[8] Yuksel, N., Saltik, B. (2023), On inextensible ruled surfaces generated via a curve derived from a curve with constant torsion, AIMS Mathematics, 8, 11312-11324. Search in Google Scholar

[9] Yildiz, O. G., Ersoy, S., Masal, M. (2014), A Note on inextensible flows of curves on oriented Surface, CUBO A Math. J., 16, 11-19. Search in Google Scholar

[10] Hussien, R. A., Gaber, S. (2016), Generated Surfaces via Inextensible Flows of Curves in ℝ³, J. Appl. Math., vol. 2016, 8 pages. Search in Google Scholar

[11] Hussien, R. A. Hussien, Youssef, T. (2016), Evolution Of Special Ruled Surfaces Via The Evolution Of Their Directrices In Euclidean 3-Space E³, Appl. Math. Inf. Sci., 10, 1949-1956. Search in Google Scholar

[12] Bas, S., Korpinar, T. (2013), Inextensible Flows of Space-like Curves on Space-like Surfaces according to Darboux Frame in M₁³, Bol. Soc. Paran. Math., 31, 9-17. Search in Google Scholar

[13] Gaber, S. (2021), New models of normal motions of the inextensible curves according to type-1 Bishop frame in ℝ³, International Journal of Geometric Methods in Modern Physics, 18, 2150009. Search in Google Scholar

[14] Korpinar, T., Altay, G., Turhan, E. (2011), New inextensible flows of tangent developable surfaces in Euclidian 3-space E³, Revista Notas de Matemática, 7, 172-17. Search in Google Scholar

[15] Tapia, V. (2009), Evolution of curvature tensors under mean curvature flow, Revista Colombiana de Matemáticas, 43, 175-185. Search in Google Scholar

[16] Asil, V., Altay, G., Korpinar T.(2016), On Inextensible Flows of New type surfaces which generated by first principle direction curve in E³, Advanced Modeling and Optimization, 18, 301-306. Search in Google Scholar

[17] Yuzbasi, Z. K., Yoon, D. W. (2018), Inextensible Flows of Curves on Lightlike Surfaces, Mathematics, 6, 224. Search in Google Scholar

[18] O’Neill, B. (2006), Elementary differential geometry, Revised second edition.Elsevier/Academic Press, Amsterdam. Search in Google Scholar

[19] Do Carmo, M. P. (1976), Differential Geometry of Curves and Surfaces, Prentice Hall, Englewood Cliffs, NJ. Search in Google Scholar