Construction and Analysis of Smarandache Curves for Integral Binormal Curves in Euclidean 3-Space

Year 2025, Volume: 8 Issue: 3 , 149 - 157 , 17.09.2025

Ayman Elsharkawy , Clemente Cesarano , Hasnaa Baizeed

https://doi.org/10.32323/ujma.1739984

https://izlik.org/JA95XF82EL

Abstract

This paper presents a detailed geometric analysis of Smarandache curves generated from integral binormal curves within three-dimensional Euclidean space. We provide a complete derivation of the Frenet apparatus encompassing tangent, normal, and binormal vectors, alongside curvature and torsion functions for four distinct types of Smarandache curves: $TN$, $TB$, $NB$, and $TNB$. Furthermore, we establish the necessary and sufficient criteria for these curves to be characterized as general helices or Salkowski curves. A significant outcome of our work is the demonstration that helical characteristics are transmitted from the original curve to its Smarandache derivatives. The theoretical framework is substantiated with numerical examples, including a circular helix and other spatial curves.

Keywords

Frenet frame , General helices , Integral curves , Salkowski curves , Smarandache curves

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