Mannheim curves and the constant-pitch curves are two specific classes of space curves that are identified by a relation between their curvature and torsion functions. We detail the construction of these two types of curves from any given arbitrary regular space curve in  by means of the so-called Combescure transformation. Further,  we show that both Mannheim and constant-pitch curves have an integral characterization in terms of a given spherical curve. This has important applications to the theory of elastic strips and elastic curves.

Combescure transformation, spherical elastic curve, Willmore surface, Hopf cylinder.