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Complete noncompact submanifolds with flat normal bundle

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Fu H.-P.

Annales Polonici Mathematici

2016

tom 116

nr 2

145-154

Let Mⁿ (n ≥ 3) be an n-dimensional complete super stable minimal submanifold in $ℝ^{n+p}$ with flat normal bundle. We prove that if the second fundamental form A of M satisfies $∫_Mi |A|^α < ∞$, where α ∈ [2(1 - √(2/n)), 2(1 + √(2/n))], then M is an affine n-dimensional plane. In particular, if n ≤ 8 and $∫_{M}| A|^d < ∞$, d = 1,3, then M is an affine n-dimensional plane. Moreover, complete strongly stable hypersurfaces with constant mean curvature and finite $L^α$-norm curvature in ℝ⁷ are considered.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Fu H.-P.

1 2016

Wyniki wyszukiwania

Complete noncompact submanifolds with flat normal bundle