Complete noncompact submanifolds with flat normal bundle

• Autorzy: Hai-Ping Fu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
• 53C40: Global submanifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2016
• Tom: 116
• Numer: 2
• Strony: 145-154

Daty

wydano

2016

Twórcy

autor

Hai-Ping Fu

• Department of Mathematics, Nanchang University, 330031 Nanchang, P.R. China

Identyfikatory

DOI

10.4064/ap3743-12-2015