Journal of East China Normal University(Natural Sc ›› 2018, Vol. 2018 ›› Issue (3): 38-45.doi: 10.3969/j.issn.1000-5641.2018.03.005

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L2 harmonic 2-forms on a hypersurface in Euclidean space

ZHANG Quan-rui, LIU Jian-cheng   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
  • Received:2017-05-01 Online:2018-05-25 Published:2018-05-29

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

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