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http://dx.doi.org/10.4134/CKMS.2008.23.3.421

RIGIDITY OF MINIMAL SUBMANIFOLDS WITH FLAT NORMAL BUNDLE  

Seo, Keom-Kyo (SCHOOL OF MATHEMATICS KOREA INSTITUTE FOR ADVANCED STUDY)
Publication Information
Communications of the Korean Mathematical Society / v.23, no.3, 2008 , pp. 421-426 More about this Journal
Abstract
Let $M^n$ be a complete immersed super stable minimal submanifold in $\mathbb{R}^{n+p}$ with fiat normal bundle. We prove that if M has finite total $L^2$ norm of its second fundamental form, then M is an affine n-plane. We also prove that any complete immersed super stable minimal submanifold with flat normal bundle has only one end.
Keywords
minimal submanifolds; Bernstein type theorem; flat normal bundle;
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Times Cited By SCOPUS : 4
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