A Study on Normal Motion of the Torus of Revolution in ℝ 3

Abstract In the present research paper, we investigate the motion of surfaces in ℝ 3 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,...

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Bibliographic Details
Published inApplied mathematics and nonlinear sciences Vol. 9; no. 1
Main Authors Gaber, Samah, Alfadhli, Norah, Mahmoud, Elsayed I.
Format Journal Article
LanguageEnglish
Published 01.01.2024
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Summary:Abstract In the present research paper, we investigate the motion of surfaces in ℝ 3 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.
ISSN:2444-8656
2444-8656
DOI:10.2478/amns.2023.2.00079