中国科学技术大学学报 ›› 2020, Vol. 50 ›› Issue (3): 294-299.DOI: 10.3969/j.issn.0253-2778.2020.03.006

• 论著 • 上一篇    下一篇

具有有限总曲率子流形的L2调和p形式

周俊东,尹松庭   

  1. 1. 中国科学技术大学数学科学学院,安徽合肥 230026; 2. 阜阳师范大学数学与统计学院,安徽阜阳 236041; 3. 铜陵学院数学与计算学院,安徽铜陵 244000
  • 收稿日期:2019-02-13 修回日期:2020-01-10 接受日期:2020-01-10 出版日期:2020-03-31 发布日期:2020-01-10

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).

摘要: 设M是n+l维Sn+l球空间中具有法从平坦n维完备子流形,则Hp(L2(M))是M上L2调和p(2≤p≤n-2) 形式空间.首先证明了如果M的总曲率小于一个正常数,则Hp(L2(M))是平凡的;其次证明了如果M的总曲率有限,则Hp(L2(M))是有限维的.

关键词: 总曲率, L2调和p形式, 子流形

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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