On focal submanifolds of isoparametric hypersurfaces and Simons formula

الأصل · EN

The focal submanifolds of isoparametric hypersurfaces in spheres are all minimal Willmore submanifolds, mostly being A-manifolds in the sense of A.Gray but rarely Ricci-parallel (QTY,LY,TY3). In this paper we study the geometry of the focal submanifolds via Simons formula. We show that all the focal submanifolds with g≥3 are not normally flat by estimating the normal scalar curvatures. Moreover, we give a complete classification of the semiparallel submanifolds among the focal submanifolds.