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Non-null space curves related by a transformation of combescure
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Journal Article
Non-null space curves related by a transformation of combescure
2025
Overview
This study investigates non-null space curves in Minkowski 3-space that are related through the Combescure transformation, a geometric operation characterized by parallel tangent vectors at corresponding points. Using the Frenet apparatus, conditions for two non-null curves to exhibit this transformation are derived, with a focus on their tangent, principal normal, and binormal vectors. The relationships reveal significant properties of curve interactions, including parallelism of Frenet vectors and connections to Bertrand curve pairs. Additionally, the effects of the Combescure transformation on curvature and torsion are analyzed and illustrated through examples. Furthermore, as an application, the conditions under which a spatial curve associated with a non-null biharmonic curve via the Combescure transformation remains biharmonic are determined and supported by relevant examples.
Publisher
University of Nis, Faculty of Sciences and Mathematics
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