We give conditions for the shadow boundary of a Riemannian submanifold $M$ to be regular. We prove that a helix hypersurface is ruled. By studying some relations between these natural submanifolds, we show that a minimal helix shadow boundary hypersurface of $M$ is totally geodesic in $M$.
"Helix, shadow boundary and minimal submanifolds." Illinois J. Math. 52 (4) 1385 - 1397, Winter 2008. https://doi.org/10.1215/ijm/1258554368