Minimal submanifolds with flat normal bundle

Abstract

Let Mⁿ (n ≤ 7) be an n-dimensional complete immersed super stable minimal submanifold in an (n + p)-dimensional Euclidean space R^n+p with flat normal bundle. We prove that if the second fundamental form A of M satisfies ∫_M |A|³ < ∞, then M is an affine n-dimensional plane.