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(L2(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.
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.
作者
周俊东
尹松庭
ZHOU Jundong;YIN Songting(School of Mathematical Sciences,University of Science and Technology of China,Hefei Anhui 230026,P.R.China;School of Mathematics and Statistics,Fuyang Normal University,Fuyang,Anhui 236041,P.R.China;Department of Mathematics and Computer Science,Tongling University Anhui 244000,P.R.China)
基金
Supported by the Natural Science Foundation of Anhui Provincia Education Department(KJ2017A341)
the Talent Project of Fuyang Normal University(RCXM201714)
the second author is supported by the Natural Science Foundation of Anhui Province of China(1608085MA03)
the Fundamental Research Funds of Tongling Xueyuan Rencai Program(2015TLXYRC09)
