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

Author:

Gaber Samah12,Alfadhli Norah1,Mahmoud Elsayed I.3

Affiliation:

1. 1 Department of Mathematics and Statistics , College of Science , King Faisal Univ., P.O. Box:400 Al-Ahsa , 31982 , Saudi Arabia

2. 2 Department of Mathematics, Faculty of Science , Assiut Univ ., Assiut , Egypt

3. 3 Department of Mathematics, Faculty of Science , Zagazig Univ ., Zagazig , Egypt .

Abstract

Abstract In the present research paper, we investigate the motion of surfaces in ℝ3 according to their curvatures. We study the motion of the torus of revolution via the normal velocity. We consider two cases: when the normal velocity is a function of both the time and the coordinates of the torus, and when it is a function of time only. We also study how the torus moves under different types of curvature flows, such as inverse mean curvature flow, inverse Gaussian curvature flow, and harmonic mean curvature flow. Moreover, we present some new applications of these flows.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science

Reference19 articles.

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

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.

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.

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

5. Nakayama, K., Wadati, M. (1993), The Motion of Surfaces, Journal of the Physical Society of Japan, 62, 1895-1901.

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