Spinor Formulation of Frenet Normal Spherical Image in Euclidean and Pseudo-Euclidean Spaces

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DOI: https://doi.org/10.28924/2291-8639-23-2025-151
Published: Jun 26, 2025
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M. Khalifa Saad, H. S. Abdel-Aziz, I. K. Youssef, Spinor Formulation of Frenet Normal Spherical Image in Euclidean and Pseudo-Euclidean Spaces, Int. J. Anal. Appl., 23 (2025), 151.

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M. Khalifa Saad, H. S. Abdel-Aziz, I. K. Youssef

Abstract

In this paper, we introduce one of the spherical images of a regular curve by translating Frenet frame vectors to the center of the unit sphere (Lorentizian sphere) of the Euclidean 3-space E3 (pseudo-Euclidean 3-space E1,2). Especially, Frenet formulas for the normal spherical image of a regular curve can be obtained in terms of spinors. As a result of this study, we found that Frenet equations for that one can be simplified to a single equation with two complex components. Finally, interesting illustrative examples of the obtained results are given and plotted.

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