Rigidity of minimal submanifolds with flat normal bundle
Commun. Korean Math. Soc. 2008 Vol. 23, No. 3, 421-426
Printed September 1, 2008
Keomkyo Seo
KIAS
Abstract : Let $M^n$ be a complete immersed super stable minimal submanifold in $\mathbb{R}^{n+p}$ with flat 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
MSC numbers : 53C42, 53A07
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