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Embankment surfaces according to the Bishop frame in Euclidean 3-space
(Univ Nis, Fac Sci Math, 2025) Kocakusakli, Erdem
This article is devoted to embankment, embankment-like and tubembankment-like surfaces determined by regular space curve according to the Bishop frame in Euclidean 3-space. First, parametric equations, quaternionic and matrix representations of them are given. Moreover, geometric properties of them are examined and some theorems and conclusions are obtained. At the end of the paper, the theory of the paper is supported by the examples and their illustrated figures are drawn by the programme Mathematica.
Embankment surfaces with the Darboux frame in Euclidean 3-space
(Amer Inst Mathematical Sciences-Aims, 2025) Kocakusakli, Erdem
This article was dedicated to the study of embankment, embankment-like, and tubembankment-like surfaces generated by a regular space curve according to the Darboux frame in Euclidean 3-space. Initially, we presented the parametric equations defining these surfaces. Subsequently, their quaternionic and matrix representations were derived to provide alternative and efficient formulations. In addition, the geometric properties of tubembankment-like surfaces were thoroughly examined, leading to several significant theorems and corollaries. To demonstrate the applicability and validity of the theoretical results, illustrative examples were generated by using the Mathematica program.