具有有限总曲率子流形的L^2调和p形式  

L^2-harmonic p-forms on submanifolds with finite total curvature

作　　者：周俊东[1,2] 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)

机构地区：[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

出　　处：《中国科学技术大学学报》2020年第3期294-299,316,共7页JUSTC

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)

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.

关 键 词：总曲率 L^2调和p形式 子流形 

分 类 号：O186.1[理学—数学]