Ortak Bertrand-B İsogeodezik Eğriye Sahip Yüzey Aileleri

Abstract

Bu çalışmada 3-boyutlu Öklid uzayında parametrik denklemi ile verilen yüzey üzerinde eğriliği sıfırdan farklı olan bir eğrinin Bertrand B-çiftinin bu yüzey üzerinde isogeodezik olması için gerekli ve yeterli şartlar elde edilerek, ortak Bertrand-B isogeodezik eğrili yüzey aileleri problemi ele alınmıştır. Bu çalışmada 3-boyutlu Öklid uzayında parametrik denklemi ile verilen yüzey üzerinde eğriliği sıfırdan farklı olan bir eğrinin Bertrand B-çiftinin bu yüzey üzerinde isogeodezik olması için gerekli ve yeterli şartlar elde edilerek, ortak Bertrand-B isogeodezik eğrili yüzey aileleri problemi ele alınmıştır.

Keywords

• Bertrand-B eğri
• Bishop 2-çatısı
• isogeodezik eğri
• parametrik yüzey

Surface Family With A Common Bertrand-B Isogeodesic Curve

Abstract

In this paper, we construct a surface family possessing a Bertrand B pair of a given curve as an geodesic curve. Using the Bishop-2 frame frame of the given Bertrand B curves, we present the surface as a linear combination of this frame and analyse the necessary and sufficient condition for a given curve such that its Bertrand B pairs is both parametric and geodesic on a parametric surface. Finally, we present some interesting examples to show the validity of this study. In this paper, we construct a surface family possessing a Bertrand B pair of a given curve as an geodesic curve. Using the Bishop-2 frame frame of the given Bertrand B curves, we present the surface as a linear combination of this frame and analyse the necessary and sufficient condition for a given curve such that its Bertrand B pairs is both parametric and geodesic on a parametric surface. Finally, we present some interesting examples to show the validity of this study.

Keywords

• Bertrand B-curves
• Bishop-2 Frame
• isogeodesic curve
• parametric surface

References

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