Complete noncompact submanifolds with flat normal bundle

Hai-Ping Fu. "Complete noncompact submanifolds with flat normal bundle." Annales Polonici Mathematici 116.2 (2016): 145-154. <http://eudml.org/doc/280710>.

@article{Hai2016,
abstract = {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.},
author = {Hai-Ping Fu},
journal = {Annales Polonici Mathematici},
keywords = {flat normal bundle; minimal submanifold; stable hypersurface},
language = {eng},
number = {2},
pages = {145-154},
title = {Complete noncompact submanifolds with flat normal bundle},
url = {http://eudml.org/doc/280710},
volume = {116},
year = {2016},
}

TY - JOUR
AU - Hai-Ping Fu
TI - Complete noncompact submanifolds with flat normal bundle
JO - Annales Polonici Mathematici
PY - 2016
VL - 116
IS - 2
SP - 145
EP - 154
AB - 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.
LA - eng
KW - flat normal bundle; minimal submanifold; stable hypersurface
UR - http://eudml.org/doc/280710
ER -