On the striction curves along the involutive and Bertrandian Darboux ruled surfaces based on the tangent vector fields

• Main Authors: Suleyman Senyurt, Şeyda Kılıçoğlu
• Format: Article
• Language: English
• Published: BİSKA Bilisim Company 2016-10-01
• Series: New Trends in Mathematical Sciences
• Subjects: Involute curve; Bertrand curves pair; striction curves; Bertrandian Darboux ruled surfaces; involutive Darboux ruled surfaces.
• Online Access: https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=7210
• ISSN: 2147-5520; 2147-5520

In this paper, we consider special ruled surfaces associated to the involute curve and Bertrand mate of a curve. They are called as Involutive Darboux Frenet ruled surface and Bertrandian Darboux Frenet ruled surface, cause of their generators are the Darboux vector fields of involute curve and Bertrand mate. We give the parametric equations of striction curves along these Frenet ruled surfaces in terms of the Frenet apparatus of curve . Further some results are given based on the tangent vector fields of these striction curves along Involutive and Bertrand Darboux ruled surfaces in E3.