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<p>This work presents a comprehensive analysis of generalized offset curves, which was motivated by the requirements of numerous engineering and modern physics problems. For this purpose, specific characteristics of generalized offsets of space curves are described in both Euclidean and Minkowski spaces. Furthermore, the generalized curves are analyzed in a more precise approximation by using the ϵ-neighborhood approach, offering a deeper understanding of their geometric transformation. Also, a variational analysis of arc length, curvature, and torsion functions is carried out for both spaces and finally, highlighting the differences between original curves and their generalized offsets. Several illustrative examples are provided to support the theoretical findings.</p>

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Comprehensive Variations of the Generalized Offset Curves for Space Curves

  • 期刊论文

  • 发表日期：

    2026年3月13日

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  • Ali Çalişkan,
  • Selcan Kocabaş

摘要

This work presents a comprehensive analysis of generalized offset curves, which was motivated by the requirements of numerous engineering and modern physics problems. For this purpose, specific characteristics of generalized offsets of space curves are described in both Euclidean and Minkowski spaces. Furthermore, the generalized curves are analyzed in a more precise approximation by using the ϵ-neighborhood approach, offering a deeper understanding of their geometric transformation. Also, a variational analysis of arc length, curvature, and torsion functions is carried out for both spaces and finally, highlighting the differences between original curves and their generalized offsets. Several illustrative examples are provided to support the theoretical findings.