Complete noncompact submanifolds with flat normal bundle

Hai-Ping Fu

Hai-Ping Fu

Annales Polonici Mathematici, Tome 116 (2016), p. 145-154 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $\int_{M} i {| A |}^{α} < \infty$ , where α ∈ [2(1 - √(2/n)), 2(1 + √(2/n))], then M is an affine n-dimensional plane. In particular, if n ≤ 8 and $\int_{M} {| A |}^{d} < \infty$ , 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.

Publié le : 2016-01-01

Zbl 1337.53079

EUDML-ID : urn:eudml:doc:280710

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     author = {Hai-Ping Fu},
     title = {Complete noncompact submanifolds with flat normal bundle},
     journal = {Annales Polonici Mathematici},
     volume = {116},
     year = {2016},
     pages = {145-154},
     zbl = {1337.53079},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3743-12-2015}
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Hai-Ping Fu. Complete noncompact submanifolds with flat normal bundle. Annales Polonici Mathematici, Tome 116 (2016) pp. 145-154. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3743-12-2015/