3-Boyutlu Minkowski Uzayında Bishop Çatısına Göre Sabit Eğrilikli Null Olmayan Regle Yüzeyler

Abstract

Bu çalışmada, 3-boyutlu Minkowski uzayında Bishop çatısına göre null olmayan regle yüzeylerin Gauss ve ortalama eğrilikleri hesaplanmış ve regle yüzeylerin sabit Gauss ve ortalama eğriliğe sahip olmaları için gerekli koşullar elde edilmiştir. Ayrıca regle yüzeylerin açılabilir ve minimal olması için denklemlerinin hangi formda olması gerektiği gösterilmiştir. Buna ilaveten teğet vektör alanı tarafından üretilen sabit ortalama eğrilikli null olmayan regle yüzeylerin dayanak eğrisinin Bishop slant helis olduğu tespit edilmiştir.

Keywords

• Regle Yüzey
• Gauss Eğriliği
• Ortalama Eğrilik
• Bishop Çatısı
• Minkowski uzayı

Non-null Ruled Surfaces with Constant Curvatures According to Bishop Frame in Minkowski 3-space

Abstract

In this study, the Gaussian and mean curvatures of non-null ruled surfaces according to Bishop frame in 3-dimensional Minkowski space are calculated and obtained the necessary conditions for their curvatures to be constant. Moreover, in case the ruled surfaces to be developable and minimal, we find parametric forms. In addition, the base curve of non-null surfaces with constant mean curvares is specified to be Bishop slant helix. In this study, the Gaussian and mean curvatures of non-null ruled surfaces according to Bishop frame in 3-dimensional Minkowski space are calculated and obtained the necessary conditions for their curvatures to be constant. Moreover, in case the ruled surfaces to be developable and minimal, we find parametric forms. In addition, the base curve of non-null surfaces with constant mean curvares is specified to be Bishop slant helix.

Keywords

• Ruled Surface
• Gaussian Curvature
• Mean Curvature
• Bishop Frame
• Minkowski space

References

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