Hypersurface constrained elasticae in Lorentzian space forms (Q277736)

Summary: We study geodesics in hypersurfaces of a Lorentzian space form \(M_1^{n + 1}(c)\), which are critical curves of the \(M_1^{n + 1}(c)\)-bending energy functional, for variations constrained to lie on the hypersurface. We characterize critical geodesics showing that they live fully immersed in a totally geodesic \(M_1^3(c)\) and that they must be of three different types. Finally, we consider the classification of surfaces in the Minkowski 3-space foliated by critical geodesics.