k-Kinematik Yüzeyler İçin Konjuge Tanjant Vektörler, Asimptotik Doğrultular, Euler Teoremi ve Dupin Göstergesi

Year 2018, Volume: 22 Issue: 6, 1559 - 1566, 01.12.2018

Yasemin Kemer Erhan Ata

https://doi.org/10.16984/saufenbilder.331231

Abstract

Bu çalışmada, 3 boyutlu Öklid uzayı E³te bir M yüzeyinin noktalarına kuaterniyonlar ile tanımlanan katı
cisim hareketi uygulanarak elde edilen bir M^g k-kinematik yüzeyini
tanımladık. Daha sonra bu yüzey için bir yüzeyi diferensiyel geometrik olarak
daha iyi anlamamızı sağlayan ait şekil operatörü, asimptotik doğrultu, konjuge
tanjant vektörler, Euler Teoremi ve Dupin göstergesi gibi önemli kavramları
hesaplayıp inceledik. 

Keywords

Asimptotik doğrultu, konjuge tanjant vektör, Dupin göstergesi, Euler teoremi.

Conjugate Tangent Vectors, Asymptotic Directions, Euler Theorem and Dupin Indicatrix For k-Kinematic Surfaces

Abstract

In this study, we define the
k-kinematic surface M^g which is obtained from
a surface M on Euclidean 3-surface E³ by applying rigid
motion described by quaternions to points of M. Then we investigate and calculate for this surface some
important concepts such as shape operator, asymptotic vectors, conjugate
tangent vectors, Euler theorem and Dupin indicatrix which help to understand a
surface differential geometrically well. 

Keywords

Asymptotic direction, conjugate tangent vectors, Dupin indicatrix, Euler theorem

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