Isotropic minimal submanifolds in a space form (Q1112347)

The author proves the following: Let M be an n-dimensional compact minimal submanifold immersed in a sphere of curvature c. If M is isotropic and the sectional curvature K of M satisfies \(nc/3(n+2)\leq K\leq c,\) then \(K\equiv c\) (i.e., M is totally geodesic) or \(K\equiv nc/2(n+1)\) (i.e., M is a Veronese submanifold of degree 2) or \(K\equiv nc/3(n+2)\) (i.e. is a Veronese submanifold of degree 3).