Developable Ruled Surfaces with Constant Mean Curvature Along a Curve

In this work, we study developable ruled surfaces with constant mean curvature along a curve. The mean curvature of developable ruled surfaces generated by indicatrix curves is calculated. The analysis is first carried out in Euclidean three-space and then extended to Lorentz space. For both geometries, we derive the necessary and sufficient conditions under which the developable ruled surfaces exhibit constant mean curvature. In addition, we calculate the mean curvature of the surface using time-like and space-like curves. Later, we give a sufficient condition for the mean curvature of a developable surface to be constant along a striction curve. Finally, we give some examples in Euclidean and Lorentz spaces and present computational examples.