On some new frames along a space curve and integral curves with Darboux q-vector fields in $ \mathbb{E}^3 $

Bahar UYAR DÜLDÜL; Bahar UYAR DÜLDÜL

doi:10.3934/math.2024869

AIMS Mathematics

2024, Volume 9, Issue 7: 17871-17885. doi: 10.3934/math.2024869

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Research article

On some new frames along a space curve and integral curves with Darboux q-vector fields in $ \mathbb{E}^3 $

Bahar UYAR DÜLDÜL ^,

Yildiz Technical University, Faculty of Education, Department of Mathematics and Science Education, Istanbul, Türkiye

Received: 20 February 2024 Revised: 30 April 2024 Accepted: 16 May 2024 Published: 24 May 2024
MSC : 53A04

In this paper, to start we defined osculating q-frame, normal q-frame, and rectifying q-frame along a space curve in Euclidean 3-space $ \mathbb{E}^3 $ by using the Darboux vector field of the q-frame. We obtained the derivative equations of these new frames. Later, we defined some new integral curves of a space curve and called them $ \overline{\mathsf{d}}_o $-direction curve, $ \overline{\mathsf{d}}_n $-direction curve and $ \overline{\mathsf{d}}_r $-direction curve. Finally, we gave some theorems and results related with these curves.
- q-frame,
- integral curve,
- osculating q-frame,
- normal q-frame,
- rectifying q-frame
Citation: Bahar UYAR DÜLDÜL. On some new frames along a space curve and integral curves with Darboux q-vector fields in $ \mathbb{E}^3 $[J]. AIMS Mathematics, 2024, 9(7): 17871-17885. doi: 10.3934/math.2024869

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Abstract

In this paper, to start we defined osculating q-frame, normal q-frame, and rectifying q-frame along a space curve in Euclidean 3-space $ \mathbb{E}^3 $ by using the Darboux vector field of the q-frame. We obtained the derivative equations of these new frames. Later, we defined some new integral curves of a space curve and called them $ \overline{\mathsf{d}}_o $-direction curve, $ \overline{\mathsf{d}}_n $-direction curve and $ \overline{\mathsf{d}}_r $-direction curve. Finally, we gave some theorems and results related with these curves.

References

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