On Hopf hypersurfaces of the complex quadric with constant principal curvatures

Abstract

In this paper, we classify the Hopf hypersurfaces of the complex quadric $Q^m=S{O}_{m+2}/(S{O}_{2}S{O}_m)$ ($m\ge 3$) with at most five distinct constant principal curvatures. We also classify the Hopf hypersurfaces of $Q^m$ ($m=3,4,5$) with constant principal curvatures. All these real hypersurfaces are open parts of homogeneous examples.

47 pages. Comments are welcome