On pseudohyperbolic space motions

Authors: TUNAHAN TURHAN, NURAL YÜKSEL, NİHAT AYYILDIZ

Abstract: In the present paper, the geometrical instantaneous invariants of the motion $H_{_{m}}/H_{_{f}}\ $in dual Lorentzian $3$-space are determined. Depending on this, the dual Lorentzian instantaneous screw axis of the motion of $K_{_{m}}$ with respect to the dual pseudohyperbolic space $K_{_{m}}$ is constructed. On the other hand, we show that, in each position of $H_{_{m}}$, the fixed and moving axodes have the instantaneous screw axis of this position in common. We also give relations between the geodetic curvature and the curvature of the polodes.

Keywords: Pseudohyperbolic space, instantaneous screw axis, Lorentzian 3-space, axodes

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