Embankment surfaces with the Darboux frame in Euclidean 3-space

Erdem Kocakuşaklı; Erdem Kocakuşaklı

doi:10.3934/math.2025937

AIMS Mathematics

2025, Volume 10, Issue 9: 20979-21003. doi: 10.3934/math.2025937

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Research article

Embankment surfaces with the Darboux frame in Euclidean 3-space

Erdem Kocakuşaklı ^{1,2
,
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1.
Department of Mathematics, Faculty of Arts and Science, Sinop University, Sinop, Turkey
2.
Department of Basic Sciences, Turkish Military Academy, National Defense University, Ankara, Turkey

Received: 19 May 2025 Revised: 17 August 2025 Accepted: 21 August 2025 Published: 12 September 2025
MSC : 53A05, 53A17, 53A55

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.
- embankment surface,
- Darboux frame,
- quaternion,
- matrix representation,
- homothetic motion
Citation: Erdem Kocakuşaklı. Embankment surfaces with the Darboux frame in Euclidean 3-space[J]. AIMS Mathematics, 2025, 10(9): 20979-21003. doi: 10.3934/math.2025937

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Abstract

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.

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