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In this paper we give geometric definitions of the Lorentzian ellipse, Lorentzian hyperbola, and Lorentzian parabola as plane curves in Lorentzian plane. Moreover we obtain the equations of Lorentzian revolution ellipsoid, Lorentzian revolution hyperboloid and Lorentzian revolution paraboloid respectively.

Conics and Quadrics in Lorentzian Space