Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-23T12:19:14.960Z Has data issue: false hasContentIssue false
  • English
  • Français

Ricci curvature and ends of Riemannian orbifolds

Part of: Global differential geometry

Published online by Cambridge University Press:  26 February 2010

Liang-Khoon Koh
Liang-Khoon Koh
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 119260, Singapore. e-mail: [email protected]
Get access

Abstract

We consider Riemannian orbifolds with Ricci curvature nonnegative outside a compact set and prove that the number of ends is finite. We also show that if that compact set is small then the Riemannian orbifolds have only two ends. A version of splitting theorem for orbifolds also follows as an easy consequence.

MSC classification

Secondary: 53C20: Global Riemannian geometry, including pinching
Type
Research Article
Information
Mathematika , Volume 45 , Issue 1 , June 1998 , pp. 135 - 144
Copyright
Copyright © University College London 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Borzellino, J.. Riemannian Geometry of Orbifolds. Ph.D thesis (University of California at Los Angeles, 1992).Google Scholar
2.Borzellino, J. and Zhu, S.. The splitting theorem for orbifolds. Illinois Journal of Mathematics, 38 (1994), 679–691.CrossRefGoogle Scholar
3.Cai, M.. Ends of Riemannian manifolds with non-negative Ricci curvature outside a compact set. Bulletin of the Amer. Math. Soc., 24 (1991), 371–277.CrossRefGoogle Scholar
4.Galloway, G.. A generalization of the Cheeger-Gromoll splitting theorem. Arch. Math., 47 (1986), 372–375.CrossRefGoogle Scholar
5.Colding, T., Cai, M. and Yang, D.. A gap theorem for ends of complete manifolds. Proceedings of the Amer. Math. Soc., 123 (95), 247–250.Google Scholar