First studied by Delaunay [1], the unduloid (or onduloid) is a surface of revolution of an elliptic catenary with constant nonzero mean curvature (in this case, the reciprocal of twice the major axis length, ). It can be obtained by tracing the focus of a rolling ellipse along a fixed line. This surface appears in fields like string theory [2] and carbon nanotubes [3].

[2] K. Maeda and U. Miyamoto, "Black Hole-Black String Phase Transitions from Hydrodynamics." arxiv:0811.2305.

[3] I. M. Mladenov, M. Ts. Hadzhilazova, V. M. Vassilev, and P. A. Djondjorov, "Unduloid-like Equilibrium Shapes of Carbon Nanotubes Subjected to Hydrostatic Pressure," Geometric Methods in Physics, Trends in Mathematics (P. Kielanowski, S. T. Ali, A. Odesskii, A. Odzijewicz, M. Schlichenmaier, and T. Voronov, eds.), Basel: Birkhauser, 2013 pp. 195–202. doi:10.1007/978-3-0348-0645-9_ 18.