Rigidity of minimal submanifolds with flat normal bundle

Let Mn (n ≥ 3) be an n-dimensional complete immersed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{{n - 2}} {n} $$\end{document}-super-stable minimal submanifold in an (n + p)-dimensional Euclidean space ℝn+p with flat normal bundle. We prove that if the second fundamental form of M satisfies some decay conditions, then M is an affine plane or a catenoid in some Euclidean subspace.