RIGIDITY OF MINIMAL SUBMANIFOLDS WITH FLAT NORMAL BUNDLE

Title & Authors
RIGIDITY OF MINIMAL SUBMANIFOLDS WITH FLAT NORMAL BUNDLE
Seo, Keom-Kyo;

Abstract
Let $\small{M^n}$ be a complete immersed super stable minimal submanifold in $\small{\mathbb{R}^{n+p}}$ with fiat normal bundle. We prove that if M has finite total $\small{L^2}$ 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;
Language
English
Cited by
1.
ON THE STRUCTURE OF MINIMAL SUBMANIFOLDS IN A RIEMANNIAN MANIFOLD OF NON-NEGATIVE CURVATURE,;;

대한수학회보, 2009. vol.46. 6, pp.1213-1219
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L2 harmonic 1-forms on minimal submanifolds in hyperbolic space, Journal of Mathematical Analysis and Applications, 2010, 371, 2, 546
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Rigidity of minimal submanifolds with flat normal bundle, Proceedings - Mathematical Sciences, 2010, 120, 4, 457
3.
ON THE STRUCTURE OF MINIMAL SUBMANIFOLDS IN A RIEMANNIAN MANIFOLD OF NON-NEGATIVE CURVATURE, Bulletin of the Korean Mathematical Society, 2009, 46, 6, 1213
4.
Bernstein type theorems for complete submanifolds in space forms, Mathematische Nachrichten, 2012, 285, 2-3, 236
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