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<p>In this paper, we describe a new modified orthogonal Saban frame for timelike and spacelike curves with geodesic curvature on <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40995_2024_1767_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(S^{2}_{1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>S</mi> <mn>1</mn> <mn>2</mn> </msubsup> </math></EquationSource> </InlineEquation> and the Saban frame for hyperbolic curves with geodesic curvature on <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40995_2024_1767_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^{2}_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>H</mi> <mn>0</mn> <mn>2</mn> </msubsup> </math></EquationSource> </InlineEquation>. We study the evolution of curves depending on the modified orthogonal Sabban frame and we obtain the necessary conditions for the inextensible flow of curves on modified orthogonal Saban frame.</p>

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A New Modified Orthogonal Saban Frame on \(S^{2}_{1}\) and \(H^{2}_{0}\) and the Evolution of Curves

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Alperen Kızılay,
  • Atakan Tuğkan Yakut

摘要

In this paper, we describe a new modified orthogonal Saban frame for timelike and spacelike curves with geodesic curvature on \(S^{2}_{1}\) S 1 2 and the Saban frame for hyperbolic curves with geodesic curvature on \(H^{2}_{0}\) H 0 2 . We study the evolution of curves depending on the modified orthogonal Sabban frame and we obtain the necessary conditions for the inextensible flow of curves on modified orthogonal Saban frame.