Evolution of space curves and the special ruled surfaces with modified orthogonal frame

Kemal Eren; Hidayet Huda Kosal; Kemal Eren; Hidayet Huda Kosal

doi:10.3934/math.2020134

AIMS Mathematics

2020, Volume 5, Issue 3: 2027-2039. doi: 10.3934/math.2020134

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Evolution of space curves and the special ruled surfaces with modified orthogonal frame

Kemal Eren ^,,
Hidayet Huda Kosal

Department of Mathematics, Faculty of Arts and Sciences, Sakarya University, Sakarya, 54187 Turkey

Received: 28 November 2019 Accepted: 13 February 2020 Published: 24 February 2020
MSC : 53A05, 53A25, 58C27

In this study, we investigate the evolution of space curves and the special ruled surfaces with modified orthogonal frame. Firstly, we recall the relations between the Serret-Frenet frame and the modified orthogonal frame. Then we investigate the evolution of space curves relative to these relations. Moreover, we determine the first and second fundamental forms, the Gaussian and mean curvatures of the tangent, normal, and binormal ruled surfaces according to the modified frame. In these regards, we obtain the characterizations of the minimal and developable ruled surfaces based on modified orthogonal frame.
- modified orthogonal frame,
- evolution of curve,
- smoke ring equations,
- ruled surfaces,
- Gaussian curvature,
- mean curvature
Citation: Kemal Eren, Hidayet Huda Kosal. Evolution of space curves and the special ruled surfaces with modified orthogonal frame[J]. AIMS Mathematics, 2020, 5(3): 2027-2039. doi: 10.3934/math.2020134

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Abstract

In this study, we investigate the evolution of space curves and the special ruled surfaces with modified orthogonal frame. Firstly, we recall the relations between the Serret-Frenet frame and the modified orthogonal frame. Then we investigate the evolution of space curves relative to these relations. Moreover, we determine the first and second fundamental forms, the Gaussian and mean curvatures of the tangent, normal, and binormal ruled surfaces according to the modified frame. In these regards, we obtain the characterizations of the minimal and developable ruled surfaces based on modified orthogonal frame.

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