CURVATURE PINCHING FOR MINIMAL SUBMANIFOLDS OF A SPHERE

Let S^{n+p}(c) be an (n + p)-dimensional Euclidean sphere of constant curvature c and M an n-dimensional minimal submanifold isometrically immersed in S^n+p(c). We want to caracterize M under the assumption of scalar curvature ρ of M satisfying ρ ≥ n(n − 1)c − np(n+ 2)]/[2(n + p + 2)].c.