Willmore surfaces foliated by time-like pseudo circles discrete dynamical systems in

In this paper, we determine all pseudo circle foliating surfaces by solution to the elastic curve equation k " + 12 k(3) + ek = 0, e = 1, 0,- 1. Especially, we also show that all pseudo circle foliating surfaces with zero mean curvature are just generalized helicoids, catenoids and pseudo Riemannian surfaces.