This paper aims to design a generalized cylinder with a geodesic base curve according to the Darboux frame in Euclidean 3-space. A generalized cylinder is a special ruled surface that is constructed by a continuous fixed motion of a generator line called the ruling along a given curve called the base curve. The necessary and sufficient conditions for the base curve to be geodesic are studied. The main results show that the generalized cylinder with a geodesic base curve is an osculating cylinder whose base curve is a helical geodesic, and the rulings are directed by the unit osculating Darboux vector.
Generalized cylinder geodesic Darboux frame general helix osculating Darboux vector
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Yayımlanma Tarihi | 31 Aralık 2021 |
Gönderilme Tarihi | 14 Aralık 2021 |
Yayımlandığı Sayı | Yıl 2021 Sayı: 37 |
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