Minkowski 3-uzayda 2. tip Bishop çatısına göre null olmayan eğrilerin karakterizasyonlarına dair bir inceleme

Year 2016, Volume: 20 Issue: 2, 325 - 335, 01.08.2016

Süha Yılmaz , Yasin Ünlütürk , Abdullah Mağden

https://doi.org/10.16984/saufenbilder.50911

Cited By: 3

Abstract

Bu çalışmada,  de Bishop çatısının yeni bir yorumuna göre null olmayan eğrilerin klasik diferensiyel geometrisini inceliyoruz. Bu yeni yorumlanan çatıya, 2. Tip Bishop çatısı şeklinde adlandırıyoruz. Öncelikle, bir adi diferensiyel denklem sistemi elde etmek suretiyle, regüler ve null olmayan eğrilerin konum vektörünü araştırıyoruz. Bu sistemin çözümü,  de 2. tip Bishop çatısın göre konum vektörünün bileşenlerini verir. Bununla birlikte, bu yeni çatıya göre birinci, ikinci ve üçüncü mertebeden Bishop düzlemlerini tanımlıyoruz ve bu düzlemlere bağlı olarak  de konum vektörlerini karakterize ediyoruz.

Keywords

spacelike eğri, timelike eğri, konum vektörü, bishop düzlemleri, 2. tip Bishop çatısı

A study on the characterizations of non-null curves according to the Bishop frame of type-2 in Minkowski 3-space

Abstract

In this work, we study classical differential geometry of non-null curves according to the new version of Bishop frame in  which we call it along the work as “the Bishop frame of type-2”. First, we investigate position vector of a regular non-null curve by obtaining a system of ordinary differential equations. The solution of the system gives the components of the position vector with respect to the Bishop frame of type-2 in . Moreover, we define the first, second and third order Bishop planes according to this new frame, and also, regardig to these planes, we characterize position vectors in . 

Keywords

Spacelike Curve, Timelike Curve, Position Vector, The Bishop Planes, The Bishop Frame of Type-2

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