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

Bu çalışmada, 3 boyutlu Öklid uzayı E3te bir M yüzeyinin noktalarına kuaterniyonlar ile tanımlanan katı cisim hareketi uygulanarak elde edilen bir Mg 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.

Anahtar Kelimeler:

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

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

In this study, we define the k-kinematic surface Mg 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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