非负Ricci曲率与开流形的拓扑(英文)  

Nonnegative Ricci curvature and topology of open manifolds

作　　者：毛显[1] 

机构地区：[1]沈阳工程学院基础教学部,沈阳110136

出　　处：《沈阳工程学院学报（自然科学版）》2010年第4期377-380,共4页Journal of Shenyang Institute of Engineering:Natural Science

摘　　要：研究了具非负Ricci曲率和大体积增长的完备非紧Riemann流形的拓扑.利用Riemann流形上距离函数的临界点理论,证明了如果截面曲率KM≥C>-∞且lim supr→∞volB[(p,r)]ωnrn-αMrn+1n-1<2-n8log2Cn+n1-1αM,则此流形就具有有限拓扑型.同时且证明了若给定常数C>0,α∈[0,2]和整数n≥2,则存在正常数ε=ε(n,C,α),只要kp(r)≥-C(1+r)α且vol[Bω(nrpn,r)]<(1+ε)αM,则此流形就与□n微分同胚.推广改进了Sha-Shen等人的结果.The topology of complete non-compact Riemann manifolds with nonnegative Ricci curvature and large volume growth are investigated.It is proved that this kind of manifolds have finite topological type if the sectional curvature bounded below and lim supr→∞volB[（p,r）]ωnrn-αMrn＋1n-12-n8log2Cn＋n1-1αMholds.It s proved that ifC0,α∈[0,2]and integern≥2are given,the positive constantε=ε（n,C,α）exists,this manifolds are diffeomorphic to inifkp（r）≥-（1 ＋Cr）αandvol[Bω（nrpn,r）]（1 ＋ε）αM.The results of Sha-Shen etc.are generalized and improved.

关 键 词：非负RICCI曲率 大体积增长 有限拓扑型 临界点 

分 类 号：O186.16[理学—数学]