Minimal submanifolds with flat normal bundle

Hai-Ping Fu

doi:10.2996/kmj/1278076337

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Home > Journals > Kodai Math. J. > Volume 33 > Issue 2 > Article

June 2010 Minimal submanifolds with flat normal bundle

Hai-Ping Fu

Kodai Math. J. 33(2): 211-216 (June 2010). DOI: 10.2996/kmj/1278076337

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Abstract

Let Mⁿ (n ≤ 7) be an n-dimensional complete immersed super stable minimal submanifold in an (n + p)-dimensional Euclidean space R^n+p with flat normal bundle. We prove that if the second fundamental form A of M satisfies ∫_M |A|³ < ∞, then M is an affine n-dimensional plane.