Helical Minimal Immersions of Compact Riemannian Manifolds into a Unit Sphere

Abstract

An isometric immersion of a Riemannian manifold $M$ into a Riemannian manifold $\overline M$ is called helical if the image of each geodesic has constant curvatures which are independent of the choice of the particular geodesic. Suppose $M$ is a compact Riemannian manifold which admits a minimal helical immersion of order $4$ into the unit sphere. If the Weinstein integer of $M$ equals that of one of the projective spaces, then $M$ is isometric to that projective space with its canonical metric.