HOLDITCH THEOREM FOR THE CLOSED SPACE CURVES IN LORENTZIAN 3-SPACE

Abstract

In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L-3. For the 1-parameter closed Lorentzian space motion in L-3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.