On kinematics of semi-Euclidean submanifolds on the plane in $E_1^3$

Yılmaz Tunçer, M. Kemal Sağel, Yusuf Yayli

In this study, we obtained an equation of homothetic motion of any smooth semi-Euclidean submanifold M on its tangent plane at the contact points, along pole curves which are trajectories of instantaneous rotation centers at the contact points. Also, we gave some remarks for the homothetic motions that are both sliding and rolling at every moment. We establish a surprising relationship between the curvatures of the moving and fixed pole curves.