Rendiconti di Matematica e delle Sue Applicazioni (Jan 2008)
Surfaces with a family of nongeodesic biharmonic curves
Abstract
The only surface whose level curves of the Gauss curvature are nongeodesic biharmonic curves and such that the gradient lines are geodesics is, up to local isometries, the revolution surface defined by Caddeo-Montaldo-Piu.