On inextensible ruled surfaces generated via a curve derived from a curve with constant torsion

Nural Yüksel; Burçin Saltık; Nural Yüksel; Burçin Saltık

doi:10.3934/math.2023573

AIMS Mathematics

2023, Volume 8, Issue 5: 11312-11324. doi: 10.3934/math.2023573

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On inextensible ruled surfaces generated via a curve derived from a curve with constant torsion

Nural Yüksel ^,,
Burçin Saltık

Department of Mathematics, Erciyes University, 38039 Kayseri, Turkey

Received: 20 December 2022 Revised: 28 February 2023 Accepted: 01 March 2023 Published: 13 March 2023
MSC : 53A05

If both the arc length and the intrinsic curvature of a curve or surface are preserved, then the flow of the curve or surface is said to be inextensible. The absence of motion-induced strain energy is the physical characteristic of inextensible curve and surface flows. In this paper, we study inextensible tangential, normal and binormal ruled surfaces generated by a curve with constant torsion, which is also called a Salkowski curve. We investigate whether or not these surfaces are minimal or can be developed. In addition, we prove some theorems which are related to inextensible ruled surfaces within three-dimensional Euclidean space.
- ruled surface,
- Gaussian curvature,
- mean curvature,
- inextensible surface,
- constant curvature
Citation: Nural Yüksel, Burçin Saltık. On inextensible ruled surfaces generated via a curve derived from a curve with constant torsion[J]. AIMS Mathematics, 2023, 8(5): 11312-11324. doi: 10.3934/math.2023573

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Abstract

If both the arc length and the intrinsic curvature of a curve or surface are preserved, then the flow of the curve or surface is said to be inextensible. The absence of motion-induced strain energy is the physical characteristic of inextensible curve and surface flows. In this paper, we study inextensible tangential, normal and binormal ruled surfaces generated by a curve with constant torsion, which is also called a Salkowski curve. We investigate whether or not these surfaces are minimal or can be developed. In addition, we prove some theorems which are related to inextensible ruled surfaces within three-dimensional Euclidean space.

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