Biharmonic curves on an invariant surface (Q1009694)

The paper studies biharmonic curves on a \(G_X\)-invariant surface \(M\subset N\), where \((N,g)\) is a three-dimensional manifold and \(X\) is a Killing vector field on \(N\). The authors generalize the results from [\textit{R. Caddeo, S. Montaldo} and \textit{P. Piu}, Rend. Mat. Appl., VII. Ser. 21, No. 1--4, 143--157 (2001; Zbl 1049.58020)], obtained for biharmonic curves on a surface of revolution, and provide the characterization of proper biharmonic orbits and derive the explicit description of proper biharmonic curves on an invariant surface with constant positive Gauss curvature.