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<p>We introduce and study an involute-evolute curve pair within a modified orthogonal frame in the context of 3D Galilean space <i>G</i><sub>3</sub> . The proposed methodology involves the investigation of the aforementioned pair of curves with respect to a modified orthogonal frame, specifically by analyzing their curvature and torsion properties. By using this approach, we derive various characterizations of these curves. The proposed findings contribute to a deeper understanding of the geometric properties and the behavior of involute-evolute curve pairs in the Galilean space, thereby offering potential applications in the differential geometry and mathematical physics.</p>

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Involute-Evolute Curves with a Modified Orthogonal Frame in the Galilean Space G3

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Ayman Elsharkawy,
  • Murat Turan,
  • Hülya Gün Bozok

摘要

We introduce and study an involute-evolute curve pair within a modified orthogonal frame in the context of 3D Galilean space G3 . The proposed methodology involves the investigation of the aforementioned pair of curves with respect to a modified orthogonal frame, specifically by analyzing their curvature and torsion properties. By using this approach, we derive various characterizations of these curves. The proposed findings contribute to a deeper understanding of the geometric properties and the behavior of involute-evolute curve pairs in the Galilean space, thereby offering potential applications in the differential geometry and mathematical physics.