Tunahan TURHAN, Nural YÜKSEL, Nihat AYYILDIZ

107113

On pseudohyperbolic space motions

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.

Anahtar Kelimeler:

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

On pseudohyperbolic space motions

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,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

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