Helix submanifolds of euclidean spaces

A submanifold of R-n whose tangent space makes constant angle with a fixed direction d is called a helix. In the first part of the paper we study helix hypersurfaces. We give a local description of how these hypersurfaces are constructed. As an application we construct (nonflat) minimal helices hypersurfaces in R-n for n > 3. In the second part we give a characterization of helix submanifolds related to the solutions of the so called eikonal differential equation. As a corollary we give necessary and sufficient conditions for a manifold M to be immersed as an helix in some Euclidean space. In the third part of this paper we study r - helices submanifolds. That is to say submanifolds such that its tangent space makes a constant angle with r linearly independent directions.