3-Boyutlu öklid uzayında bertrand eğriler ve bishop çatısı

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.

Anahtar Kelimeler:

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

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

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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