Journal of University of Science and Technology of China ›› 2020, Vol. 50 ›› Issue (3): 294-299.DOI: 10.3969/j.issn.0253-2778.2020.03.006

• Original Paper • Previous Articles     Next Articles

L2-harmonic p-forms on submanifolds with finite total curvature

  

  1. ZHOU Jundong,2, YIN Songting3
  • Received:2019-02-13 Revised:2020-01-10 Accepted:2020-01-10 Online:2020-03-31 Published:2020-01-10
  • Contact: ZHOU Jundong
  • About author:ZHOU Jundong(Corresponding author), male, born in 1983, PhD/associate professor. Research field: Algebraic coding. E-mail: zhoujundong109@163.com
  • Supported by:
    Supported by the Natural Science Foundation of Anhui Provincia Education Department (KJ2017A341) and the Talent Project of Fuyang Normal University (RCXM201714), the second author is supported by the Natural Science Foundation of Anhui Province of China (1608085MA03) and the Fundamental Research Funds of Tongling Xueyuan Rencai Program (2015TLXYRC09).

Abstract: Let M be an n-dimensional complete submanifold with flat normal bundle in an (n+l)-dimensional sphere Sn+l. Let Hp(L2(M)) be the space of all L2-harmonic p-forms (2≤p≤n-2) on M. Firstly, we show that Hp(L2(M)) is trivial if the total curvature of M is less than a positive constant depending only on n. Secondly, we show that the dimension of Hp(L2(M)) is finite provided the total curvature of M is finite.

Key words: Total curvature, L2-harmonic p-form, Submanifold

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