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

Abstract

In this study, we define thek-kinematic surface Mgwhich is obtained froma surface M on Euclidean 3-surface E3by applying rigidmotion described by quaternions to points of M. Then we investigate and calculate for this surface someimportant concepts such as shape operator, asymptotic vectors, conjugatetangent vectors, Euler theorem and Dupin indicatrix which help to understand asurface differential geometrically well.

Keywords

• asimptotik doğrultu
• konjuge tanjant vektör
• dupin göstergesi
• euler teoremi.
• asymptotic direction
• conjugate tangent vectors
• dupin indicatrix
• euler theorem