Abstract.
In the Lorentzian plane, we give Cauchy-length formulas to the envelope of a family of lines. Using these, we prove the length of the enveloping trajectories of non-null lines under the planar Lorentzian motions and give the Holditch-type theorems for the length of the enveloping trajectories. Furthermore, Holditch-type theorem for the orbit areas of three collinear points which is given by Yüce and Kuruoğlu [8] is generalized to three non-collinear points.
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Received: April 28, 2008. Revised: June 3, 2008.
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Yüce, S., Kuruoğlu, N. Cauchy Formulas for Enveloping Curves in the Lorentzian Plane and Lorentzian Kinematics. Results. Math. 54, 199–206 (2009). https://doi.org/10.1007/s00025-008-0303-7
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DOI: https://doi.org/10.1007/s00025-008-0303-7