时间:2022-07-27 07:53:41
摘要研究空间形式Sn+p(1)中平均曲率与纯量曲率成线性关系的n维完备非紧子流形Mn,所得定理A将有关文献中关于常数纯量曲率的完备非紧子流形的脐性性质推广到了平均曲率与纯量曲率成线性关系的完备非紧子流形.
关键词完备非紧; 子流形;平均曲率;纯量曲率;全脐性质;空间形式
中图分类号O186.17文献标识码A文章编号1000-2537(2013)02-0008-05
文献[1~2]首先研究了正曲率空间形式中紧致闭子流形为全脐或有全脐乘积分解的一种充分条件.随后,文献[3~4]等对此作了进一步研究.之后,文献[5]研究了空间形式中常纯量曲率的完备非紧子流形.
本文进一步得到如下定理A,定理A推广并改进了定理1的结论.
定理A设Mn是空间形式Sn+p(1)中连通的完备非紧等距浸入子流形且单位平均曲率向量在法丛中平行.设Mn的平均曲率H在Mn上达到最大值而且纯量曲率R与平均曲率H在Mn上成一般线性关系aR+bH=c,其中a,b,c为常数且a,b不同时为零,而当a≠0有ca≥n(n-1).则定理1中的结论也成立.
1准备知识和若干引理
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