Some Characterizations of Spherical Indicatrix Curves Generated by Sannia Frame

Yıl 2021, Cilt: 9 Sayı: 2, 222 - 232, 15.10.2021

Süleyman Şenyurt , Kebire Hilal Ayvacı , Davut Canlı

Öz

In this study, we have first provided the relations between the Frenet frame and Sannia frame on the striction points of four ruled surfaces of
each formed by taking the basis as the tangent, normal, binormal and Darboux vector. Second, we have defined the relations between the
Sannia vectors and their derivatives. For each Sannia frame, we have calculated the Darboux frame and expressed those in terms of Frenet
frame. Last, we have obtained the arc lengths and the geodesic curvatures according to both Euclidean space E3 and unit sphere S2 of Sannia
vectors for each four of ruled surfaces.

Anahtar Kelimeler

Ruled surface, Sannia frame, Striction curve, Spherical indicatrix, Geodesic curvature.

Kaynakça

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