3-Boyutlu öklid uzayında bertrand eğriler ve bishop çatısı

Year 2017, Volume: 21 Issue: 6, 1140 - 1145, 01.12.2017

Ayşe Zeynep Azak , Melek Masal

https://doi.org/10.16984/saufenbilder.267557

Cited By: 2

Abstract

Bu çalışmada 1975 yılında L. R.
Bishop tarafından tanımlanan Bishop çatısına ait eğrilikliklerin geometrik
anlamları verildi. Daha sonra 1850 yılında Bertrand’ın tanımladığı Bertrand
eğri çiftlerinin Bishop vektörleri arasındaki bağıntılar elde edildi. Ayrıca bu
Bertrand eğri çiftlerinin paralel eğri olması durumunda bazı ilginç sonuçlar
elde edildi.

Keywords

Bertrand eğrileri, Bishop çatısı, Frenet çatısı, Öklid uzayı, paralel eğriler

Bertrand curves and bishop frame in the 3-dimensional euclidean space

Abstract

In this paper, the geometric
meanings of the curvatures belong to Bishop frame, which was defined by L.R.
Bishop in 1975, has been given. Afterwards, the relations between the Bishop
vectors of Bertrand curve couple, which Bertrand defined in 1850, has been
obtained. Furthermore, some interesting results have been found when these
curves become parallel curves.

Keywords

Bertrand curves, Bishop frame, Frenet frame, Euclidean space, parallel curves

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