数学杂志
數學雜誌
수학잡지
JOURNAL OF MATHEMATICS
2012年
4期
629-636
,共8页
黎曼流形%Ricci曲率%次大体积增长%有限拓扑型
黎曼流形%Ricci麯率%次大體積增長%有限拓撲型
려만류형%Ricci곡솔%차대체적증장%유한탁복형
Riemannian manifold%Ricci curvature%sub-large volume growth%finite topological type
本文研究了具有非负Ricci曲率和次大体积增长的完备黎曼流形的拓扑结构问题.利用Toponogov型比较定理及临界点理论,获得了流形具有有限拓扑型的结果,推广了H.Zhan和Z.Shen的定理,并且还证明了该流形的基本群是有限生成的.
本文研究瞭具有非負Ricci麯率和次大體積增長的完備黎曼流形的拓撲結構問題.利用Toponogov型比較定理及臨界點理論,穫得瞭流形具有有限拓撲型的結果,推廣瞭H.Zhan和Z.Shen的定理,併且還證明瞭該流形的基本群是有限生成的.
본문연구료구유비부Ricci곡솔화차대체적증장적완비려만류형적탁복결구문제.이용Toponogov형비교정리급림계점이론,획득료류형구유유한탁복형적결과,추엄료H.Zhan화Z.Shen적정리,병차환증명료해류형적기본군시유한생성적.
In this paper,we study the topology of complete Riemannian manifolds with nonnegative Ricci curvature and sub-large volume growth.By Toponogov's comparison theorems and critical point theory,we obtain some results on finite topological type,which improve the theorem proved by H.Zhan and Z.Shen.We also prove that such a manifold has a finitely generated fundamental group.
