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

Özet

In this study, we define the k-kinematic surface Mg which is obtained from a surface M on Euclidean 3- space 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.