Helical geodesic immersions of semi-Riemannian manifolds

Abstract

We obtain some basic results on helical geodesic immersions in semi-Riemannian geometry. For example, it is shown that, for an indefinite semi-Riemannian submanifold, if any space-like geodesics of the submanifold are helices of order d, curvatures λ₁,...,λ_d-1 and signatures ε₁,...,ε_d in the ambient space, then any time-like geodesics of the submanifold have the same order and curvatures, and signatures (-1)¹ε₁,...,(-1)^dε_d.