On pseudohyperbolic space motions

Authors

TUNAHAN TURHAN
NURAL YÜKSEL
NİHAT AYYILDIZ

DOI

10.3906/mat-1503-37

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

First Page

750

Last Page

762

Recommended Citation

TURHAN, TUNAHAN; YÜKSEL, NURAL; and AYYILDIZ, NİHAT (2015) "On pseudohyperbolic space motions," Turkish Journal of Mathematics: Vol. 39: No. 5, Article 12. https://doi.org/10.3906/mat-1503-37
Available at: https://journals.tubitak.gov.tr/math/vol39/iss5/12