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

OpenAlex İngilizce

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.