T-pedal ruled surface with the Frenet frame of the original curve in $ E^3 $

A. Elsharkawy; H. K. Elsayied; M. E. Desouky; C. Cesarano; A. Elsharkawy; H. K. Elsayied; M. E. Desouky; C. Cesarano

doi:10.3934/math.20251134

AIMS Mathematics

2025, Volume 10, Issue 11: 25606-25623. doi: 10.3934/math.20251134

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T-pedal ruled surface with the Frenet frame of the original curve in $ E^3 $

1.
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
2.
Mathematics Department, Faculty of Education, Ain-Shams University, Cairo, Egypt
3.
Section of Mathematics, International Telematic University Uninettuno, Roma, Italy

Received: 21 August 2025 Revised: 18 October 2025 Accepted: 03 November 2025 Published: 06 November 2025
MSC : 53A04, 53A55, 53A17

This paper presents a geometric study of three types of ruled surfaces generated from the tangent, normal, and binormal unit vectors of unit speed space curves. Using the T-pedal curve construction as a foundation, we analyze these surfaces through their fundamental geometric forms, including curvature properties, the striction curve geometry, and the distribution parameter. The theoretical framework is used to analyze problems in computational geometry and shape modeling, with results relevant to both mathematical research and engineering applications. The work establishes fundamental geometric insights while providing tools for applied shape modeling and analysis.
- Frenet frame,
- space curves,
- T-pedal curve,
- ruled surfaces,
- developable surface,
- minimal surface
Citation: A. Elsharkawy, H. K. Elsayied, M. E. Desouky, C. Cesarano. T-pedal ruled surface with the Frenet frame of the original curve in $ E^3 $[J]. AIMS Mathematics, 2025, 10(11): 25606-25623. doi: 10.3934/math.20251134

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Abstract

This paper presents a geometric study of three types of ruled surfaces generated from the tangent, normal, and binormal unit vectors of unit speed space curves. Using the T-pedal curve construction as a foundation, we analyze these surfaces through their fundamental geometric forms, including curvature properties, the striction curve geometry, and the distribution parameter. The theoretical framework is used to analyze problems in computational geometry and shape modeling, with results relevant to both mathematical research and engineering applications. The work establishes fundamental geometric insights while providing tools for applied shape modeling and analysis.

References

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