Helices and isometric immersions

Abstract

Let $f:M\rightarrow\tilde{M}$ be an isometric immersion of a Riemannian manifold $M$ into a Riemannian manifold $\tilde{M}$. We study the geometry of submanifolds under various assumptions with respect to the first curvature $\tilde{\lambda}_{1}$ and the second curvature $\tilde{\lambda}_{2}$ of $\tilde{\sigma}=f\circ\sigma$ in $\tilde{M}$ for a helix $\sigma$ in $M$.