Ruled Surfaces With W-direction Curves

Abstract

In this study, some special ruled surfaces were determined which were constituted by using the base curve as the W-direction curves of a Frenet curve. We gave the characterizations of developability and minimality of these ruled surfaces. We investigated the relation between the primary curve and the base curve of ruled surfaces, we also inquired the occurence geodesic curve, asymptotic line and principal line of the W-direction curve on the ruled surface. Terminally, some examples were given.

Keywords

• Ruled surface,W-direction curve,Asymptotic curve,Geodesic curve,Line of curvature

W-Yönlü Eğrilerden Elde Edilen Regle Yüzeyler

Abstract

Bu çalışmada, bir Frenet eğrisinin W-yönlü eğrisi dayanak eğrisi olarak kullanılıp elde edilen bazı özel regle yüzeyler tanımlanmıştır. Bu regle yüzeylerin açılabilirlik ve minimallik karakterizasyonlarını verdik. Esas eğri ve regle yüzeyin dayanak eğrisi arasındaki ilişkiyi, dayanak eğrisinin geodezik eğri, asimptotik eğri ve eğrilik çizgisi olması açısından inceledik. Ayrıca bazı örnekler de verildi.

Keywords

• Regle yüzey,W-yönlü yüzey,Asimptotik eğri,Geodezik eğri,Eğrilik çizgisi

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