On parallel p-equidistant ruled surfaces by using mofied orthogonal frame with curvature in E³

Muhammed T Sariaydin,Vedat Asil,Talat Korpinar

doi:10.5269/bspm.40601

Muhammed T Sariaydin, Vedat Asil + Show 1 more

Open Access

https://doi.org/10.5269/bspm.40601

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Abstract

In this paper, it is investigated Ruled surfaces according to modified orthogonal frame with curvature in 3-dimensional Euclidean space. Firstly, we give apex angle, pitch and drall of closed ruled surface in E³. Then, it characterized the relationship between these invariant of parallel p-equidistant ruled surfaces.

Highlights

Τ e2 (s), κκ e3 (s) where a dash denotes the differentation with respect to arc length s and τ (s) =
The drall PX, the striction γ, the apex angle λX and the pitch IX of the closed ruled surface are defined by det
If the e ande vectors are parallel and the distance p between central planes in suitable points are constant, this couple ruled surface are called parallel p-equidistant ruled surfaces according to modified orthogonalp frame

Summary

Introduction

The drall PX , the striction γ, the apex angle λX and the pitch IX of the closed ruled surface are defined by det 3. On Parallel p-Equidistant Surfaces in E3 Let α and αbe two regular curves and let {e1, e2, e3} and { ̃e1, ̃e2, ̃e3} be the modified orthogonal frames with curcature of α and αat the points α (s) and α (s), respectively, in E3. Let γ, γand κ, τ , κ, τbe striction curves and curvatures of R and Rruled surfaces, respectively.

Results

Conclusion