The characterizations of time-like loxodromes on time-like helicoidal surfaces in Minkowski n- space

In this thesis; the characterizations of space-like loxodromes on type I, type II and type III on time-like helicoidal surfaces in Minkowski space are studied. In the first part of this study; the definition, importance and historical development of loxodromes are given. In addition, a historical summary of some studies on loxodromes is given. In the second chapter; some basic definitions and formulas about curves and surfaces in Minkowski space are given. In addition, the parametrizations of three types of helicoidal surfaces in Minkowski space are given and the coefficents of first fundamental form are calculated. In the third part; the differential equations of the timelike loxodromes on the timelike helicoidal surface with the spacelike meridian are obtained and their general solutions are obtained. In Minkowski space, there are only timelike right helicoidal surfaces of type I which have spacelike meridians. Therefore, only the parametrizations and arc-lengths of the timelike loxodromes on these surfaces have been obtained. In the fourth part of the thesis; similarly, general solutions of differential equations determining timelike loxodromes on timelike helicoidal surface which have timelike meridians are found. In Minkowski space, there are only timelike right helicoidal surfaces of type II which have timelike meridians. Therefore, only the parametrizations of the timelike loxodromes on these surfaces are determined and the arc-lengths are obtained. Finally, an example is given to better understand the results which are obtained.