Isometric immersions with geodesic normal sections in semi-Riemannian geometry (Q1012445)

Let \(\tilde{M}\) be a Riemannian space form and \(f:M\rightarrow \tilde{M}\) an isometric immersion with geodesic normal section. It is known that in Riemannian geometry all geodesics of \(M\) have the same proper order in \(\tilde{M}\). However this does not hold when \(\tilde{M}\) is an indefinite semi-Riemannian manifold. In this paper, the authors proves sufficient conditions for an isometric immersion with geodesic normal to be helical.