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RIGIDITY OF MINIMAL SUBMANIFOLDS WITH FLAT NORMAL BUNDLE

  • Seo, Keom-Kyo
  • Published : 2008.07.31

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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  2. Rigidity of minimal submanifolds with flat normal bundle vol.120, pp.4, 2010, https://doi.org/10.1007/s12044-010-0039-7
  3. ON THE STRUCTURE OF MINIMAL SUBMANIFOLDS IN A RIEMANNIAN MANIFOLD OF NON-NEGATIVE CURVATURE vol.46, pp.6, 2009, https://doi.org/10.4134/BKMS.2009.46.6.1213
  4. Bernstein type theorems for complete submanifolds in space forms vol.285, pp.2-3, 2012, https://doi.org/10.1002/mana.201000039