%A ZHANG Quan-rui, LIU Jian-cheng
%T *L*^{2} harmonic 2-forms on a hypersurface in Euclidean space
%0 Journal Article
%D 2018
%J Journal of East China Normal University(Natural Science)
%R 10.3969/j.issn.1000-5641.2018.03.005
%P 38-45
%V 2018
%N 3
%U {https://xblk.ecnu.edu.cn/CN/abstract/article_25505.shtml}
%8 2018-05-25
%X In this paper, we study *L*^{2} harmonic 2-forms on a complete hypersurface *M* of Euclidean space **R**^{n+1}(*n* ≥ 3). By applying the Bochner technique, we prove that if the *L*^{n}(*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 *L*^{2} harmonic 2-forms on *M* are parallel. Furthermore, if *M* is a non-minimal hypersurface, then there is no nontrivial *L*^{2} harmonic 2-form on *M*.