Timelike loxodromes on Lorentzian helicoidal surfaces in Minkowski n-space

Abstract

In this paper, we examine timelike loxodromes on three kinds of Lorentzian helicoidal surfaces in Minkowski nn-space. First, we obtain the first order ordinary differential equations which determine timelike loxodromes on the Lorentzian helicoidal surfaces in En1E1n according to the causal characters of their meridian curves. Then, by finding general solutions, we get the explicit parametrizations of such timelike loxodromes. In particular, we investigate the timelike loxodromes on the three kinds of Lorentzian right helicoidal surfaces in En1E1n. Finally, we give an example to visualize the results.