On Bishop Frames of Any Regular Curve in Euclidean 3-Space

Year 2024, , 23 - 33, 27.02.2024

Sümeyye Gür Mazlum

https://doi.org/10.35414/akufemubid.1343172

Abstract

Relationships between type-1 Bishop and Frenet, type-2 Bishop and Frenet, alternative and Frenet, N-Bishop and alternative frames of any regular curve in Euclidean 3-space are known. In this study, relationships between N-Bishop and Frenet frames and relationships between type-1 Bishop, type-2 Bishop and N-Bishop frames of any regular curve in Euclidean 3-space are given. In addition, pole vectors (unit vectors in the direction of Darboux vectors) belonging to these frames are computed. Last, pole and Darboux vectors belonging to these frames are compared with each other.

Keywords

type-1 Bishop frame, Type-2 Bishop frame, alternatif frame, N-Bishop frame, Frenet frame, darboux vektörü

3-Boyutlu Öklid Uzayında Regüler Bir Eğrinin Bishop Çatıları Üzerine

Abstract

3-boyutlu Öklid uzayında herhangi bir regüler eğrinin tip-1 Bishop ve Frenet, tip-2 Bishop ve Frenet, alternatif ve Frenet, N-Bishop ve alternatif çatıları arasındaki ilişkiler bilinmektedir. Bu çalışmada, 3-boyutlu Öklid uzayında herhangi bir regüler eğrinin N-Bishop ve Frenet çatıları arasındaki ilişkiler ve tip-1 Bishop, tip-2 Bishop ve N-Bishop çatıları arasındaki ilişkiler verilmiştir. Ayrıca bu çatılara ait pol vektörleri (Darboux vektörü yönündeki birim vektörler) hesaplanmıştır. Son olarak pol ve Darboux vektörleri birbirleriyle karşılaştırılmıştır.

Keywords

tip-1 Bishop çatısı, tip-2 Bishop çatısı, alternatif çatı, N-Bishop çatısı, frenet çatısı, Darboux vektörü

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