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Rigidity of minimal submanifolds with flat normal bundle

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대한수학회 (The Korean Mathematical Society)|2008.07|대한수학회논문집 (Communications of the KMS)|제23권 제3호|pp. 421-426

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참고문헌

키워드

minimal submanifoldsBernstein type theoremflat normal bundle
주제분류수학

초록

Let Mn be a complete immersed super stable minimal submanifold in Rn+p with flat normal bundle. We prove that if M has finite total L2 norm of its second fundamental form, then M is an affine nplane. We also prove that any complete immersed super stable minimal submanifold with flat normal bundle has only one end.

Abstract

Let Mn be a complete immersed super stable minimal submanifold in Rn+p with flat normal bundle. We prove that if M has finite total L2 norm of its second fundamental form, then M is an affine nplane. We also prove that any complete immersed super stable minimal submanifold with flat normal bundle has only one end.

참고문헌 (14)

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  10. K. Smoczyk, "Bernstein type theorems with flat normal bundle", Calc. Var. PDE, 26, pp.57~67 (2006)
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