Journal of East China Normal University(Natural Science) >

2018 , Vol. 2018 >Issue 3: 38 - 45

DOI: https://doi.org/10.3969/j.issn.1000-5641.2018.03.005

L2 harmonic 2-forms on a hypersurface in Euclidean space

  • ZHANG Quan-rui ,
  • LIU Jian-cheng
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  • College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received date: 2017-05-01

  Online published: 2018-05-29

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Abstract

In this paper, we study L2 harmonic 2-forms on a complete hypersurface M of Euclidean space Rn+1(n ≥ 3). By applying the Bochner technique, we prove that if the Ln(M) norms of the traceless second fundamental form Φ and the mean curvature vector H are both bounded from above by certain constants which depend only on n, then the L2 harmonic 2-forms on M are parallel. Furthermore, if M is a non-minimal hypersurface, then there is no nontrivial L2 harmonic 2-form on M.

Key words： Euclidean space; hypersurface; L2 harmonic 2-forms; non-minimal

Cite this article

ZHANG Quan-rui , LIU Jian-cheng . L2 harmonic 2-forms on a hypersurface in Euclidean space[J]. Journal of East China Normal University(Natural Science), 2018 , 2018(3) : 38 -45 . DOI: 10.3969/j.issn.1000-5641.2018.03.005

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