Rigidity of Minimal Submanifolds with Flat Normal Bundle

Proceedings Mathematical Sciences

Hai-Ping Fu¹ 

[1] Department of Mathematics, Nanchang University, Nanchang 00, People’s Republic of China$$

关键词: Catenoid;    minimal submanifolds;    flat normal bundle.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let $M^n(n≥ 3)$ be an 𝑛-dimensional complete immersed $frac{n-2}{n}$-superstable minimal submanifold in an $(n+p)$-dimensional Euclidean space $mathbb{R}^{n+p}$ 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.

【 授权许可】

Unknown