j. inst. sci. and tech. Journal of the Institute of Science and Technology 2536-4618 Igdir University 10.21597/jist.566855 Mathematical Sciences Matematik A New Approach for Designing Ruled Surface Using the Curvature Theory Eğrilik Teorisi Kullanarak Regle Yüzey Tasarlamada Yeni Bir Yaklaşım https://orcid.org/0000-0002-5107-8436 Güler Fatma Ondokuz Mayıs Üniversitesi, Fen Edebiyat Fakültesi 12 01 2019 9 4 2200 2206 05 17 2019 07 23 2019 Copyright © 2011, Journal of the Institute of Science and Technology 2011 Journal of the Institute of Science and Technology

In this paper, we obtain new approach ruled surface generated by a curve on the surface of sphere called the spherical indicatrix. We expressed ruled surface which the striction curve of the surface will be taken as the base curve using the generator trihedron. We have given theorems for to be the asymptotic and geodesic curve on the surface of the striction curve using the curvature theory of the ruled surfaces. Also, we have calculated the Gaussian and the mean curvature of the ruled surface. We illustrate ruled surface generated by a curve on the surface of sphere called the spherical indicatrix.

Bu çalışmada küresel gösterge eğrisi tarafından üretilen regle yüzeyler için yeni bir yaklaşım elde edildi. Üreteç çatısı yardımıyla striksiyon eğrisi dayanak eğrisi olarak alınan regle yüzey araştırıldı. Regle yüzeylerin eğrilik teorisi kullanılarak striksiyon eğrisinin yüzey üzerinde geodezik eğri ve asimptotik eğri olması için teoremler verildi. Ayrıca, regle yüzeyin Gauss ve ortalama eğrilikleri ile temel formları hesaplandı. Küresel gösterge eğrisi tarafından üretilen regle yüzeye örnek verildi.

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