Prolonged Kovaryant Türevi Kullanarak Weyl uzayındaki Bir Eğrinin Tip-1 Bishop Çatısına Göre Küresel Resimlerinin İncelenmesi

Abstract

Bu çalışmada, Weyl uzayındaki bir eğrinin tip-1 Bishop çatısına göre küresel resimlerini inceledik. Ayrıca, Frenet-Serret ve tip-1 Bishop çatı aparatları arasındaki bağıntıları ifade ettik. Prolonged kovaryant türevi kullanarak, Weyl uzayında genel helis, slant helis, küresel eğri ve ayrıca çember kavramlarını tanımladık. Daha sonra, bu küresel resimlerin yukarıdaki tanımları sağlaması halinde, elde edilen şartlar birinci ve ikinci eğrilikler ve dolayısıyla Bishop eğrilikleri cinsinden ifade edildi. Bunlara ek olarak, bir eğrinin 𝑛1 ve 𝑛2 Bishop küresel resimlerinin Frenet-Serret vektör alanlarının oluşturduğu şebekenin, birinci cins Chebyshev şebekesi olma şartı ele alındı .

Keywords

• Weyl uzayı
• Genel helis
• Slant helis
• Küresel eğri
• Küresel resim.

Investigating Spherical Images of a Curve According to Type-1 Bishop Frame in Weyl Space Using Prolonged Covariant Derivative

Abstract

In this study, we investigated spherical images of a curve according to type-1 Bishop frame in three dimensional Weyl space. Further, we expressed the relations among Frenet-Serret and type-1 Bishop frame apparatus. We defined the concepts of general helix, slant helix, spherical curve and also circle by using prolonged covariant derivative in Weyl space. Later, provided that these spherical images satisfy the above definitions, the conditions obtained were expressed in terms of first and second curvatures and hence Bishop curvatures. Additionally, the condition of being Chebyshev net of the first kind of the net which is occurred with Frenet-Serret vector fields of the 𝑛1 and 𝑛2 Bishop spherical images of a curve was discussed.

Keywords

• Weyl space
• General helix
• Slant helix
• Spherical curve
• Spherical image.

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