Complete Hypersurfaces of Constant Isotropic Curvature in Space Forms

Abstract

We classify complete orientable hypersurfaces of constant isotropic curvature in space forms. We show that such a hypersurface has constant mean curvature only if it is an isoparametric hypersurface, and that it is minimal if and only if it is totally geodesic or it is the Clifford minimal hypersurface ${\mathbb{S}}^3(\frac{4c}{3})\times {\mathbb{S}}^1(4c)$ in ${\mathbb{S}}^5(c).$

arXiv comment12 Pages. Minor errors have been corrected and new examples are added