Biharmonic curves on an invariant surface
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.
scientific article; zbMATH DE number 5539482
scientific article