Integrability for the Rotation Minimizing Formulas in Euclidean 3-Space and Its Applications

Fırat YERLİKAYA; İsmail AYDEMİR

doi:https://doi.org/10.36890/iejg.621588

Makale detayları

Integrability for the Rotation Minimizing Formulas in Euclidean 3-Space and Its Applications

Yazarlar:

Fırat YERLİKAYA | İsmail AYDEMİR

Yayıncı:

Kazım İLARSLAN

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Geometry 2020 Vol.13 Issue 1, pp.116-128

Belge Tipi:

Makale

Yayın Tarihi:

1/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000471710

Sıklık:

İki Yıllık

eISSN:

1307-5624

DOI:

https://doi.org/10.36890/iejg.621588

Özet:

 

We analyze integrability for the derivative formulas of the rotation minimizing frame in the Euclidean 3-space from a viewpoint of rotations around axes of the natural coordinate system. We give a theorem that presents only one component of the indirect solution of the rotation minimizing formulas. Using this theorem, we find a lemma which states the necessary condition for the indirect solution to be a steady solution. As an application of the lemma, the natural representation of the position vector field of a smooth curve whose the rotation minimizing vector field (or the Darboux vector field) makes a constant angle with a fixed straight line in space is obtained. Also, we realize that general helices using the position vector field consist of slant helices and Darboux helices in the sense of Bishop.

Makale detayları

Integrability for the Rotation Minimizing Formulas in Euclidean 3-Space and Its Applications

Yazarlar: Fırat YERLİKAYA | İsmail AYDEMİR

Yayıncı: Kazım İLARSLAN

Ana Başlıklar: Matematik

Dergi: International Electronic Journal of Geometry 2020 Vol.13 Issue 1, pp.116-128

Belge Tipi: Makale

Yayın Tarihi: 1/2020

Belge Dili: İngilizce

Document ID (Org No.): 2000471710

Sıklık: İki Yıllık

eISSN: 1307-5624

DOI: https://doi.org/10.36890/iejg.621588

Sayı

Yazarlar:

Fırat YERLİKAYA | İsmail AYDEMİR

Yayıncı:

Kazım İLARSLAN

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Geometry 2020 Vol.13 Issue 1, pp.116-128

Belge Tipi:

Makale

Yayın Tarihi:

1/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000471710

Sıklık:

İki Yıllık

eISSN:

1307-5624

DOI:

https://doi.org/10.36890/iejg.621588