Hypersurface Constrained Elasticae in Lorentzian Space Forms

Abstract EN

We study geodesics in hypersurfaces of a Lorentzian space form M1n+1(c), which are critical curves of the M1n+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 M13(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.