PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Complete noncompact submanifolds with flat normal bundle

Volume 116 / 2016

Hai-Ping Fu Annales Polonici Mathematici 116 (2016), 145-154 MSC: Primary 53C40; Secondary 53C42. DOI: 10.4064/ap3743-12-2015 Published online: 2 December 2015

Abstract

Let $M^n$ $(n\geq 3)$ be an $n$-dimensional complete super stable minimal submanifold in $\mathbb {R}^{n+p}$ with flat normal bundle. We prove that if the second fundamental form $A$ of $M$ satisfies $\int _M|A|^\alpha <\infty $, where $\alpha \in [2(1-\sqrt {2/n}), 2(1+\sqrt {2/n})]$, then $M$ is an affine $n$-dimensional plane. In particular, if $n\leq 8$ and $ \int _{M}|A|^d<\infty $, $d=1,3,$ then $M$ is an affine $n$-dimensional plane. Moreover, complete strongly stable hypersurfaces with constant mean curvature and finite $L^\alpha $-norm curvature in $\mathbb {R}^{7}$ are considered.

Authors

  • Hai-Ping FuDepartment of Mathematics
    Nanchang University
    330031 Nanchang, P.R. China
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image