Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Closed geodesics and volume growth of Riemannian manifolds


Author: Jianming Wan
Journal: Proc. Amer. Math. Soc. 139 (2011), 687-689
MSC (2010): Primary 53C20; Secondary 53C22
DOI: https://doi.org/10.1090/S0002-9939-2010-10549-X
Published electronically: August 24, 2010
MathSciNet review: 2736348
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we study the relation between the existence of closed geodesics and the volume growth of open Riemannian manifolds with non-negative curvature.


References [Enhancements On Off] (What's this?)

  • 1. J. Cheeger and D. Ebin, Comparison Theorems in Riemannian Geometry. North-Holland, Amsterdam, 1975. MR 0458335 (56:16538)
  • 2. J. Cheeger and D. Gromoll, The structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96, 413-443, 1972. MR 0309010 (46:8121)
  • 3. M. W. Hirsch, Differential Topology. Springer-Verlag, 1976. MR 0448362 (56:6669)
  • 4. W. Klingenberg, Riemannian Geometry. de Gruyter, 1982. MR 666697 (84j:53001)
  • 5. V. B. Marenich and V. A. Toponogov, Open manifolds of nonnegative Ricci curvature with rapidly growing volume (Russian). Sib. Mat. Zh. 26, no. 4 (152), 191-194, 1985. MR 0804031 (86k:53061)
  • 6. D. Ordway, B. Stephens and D. G. Yang, Large volume growth and finite topological type, Proceedings of the A.M.S. 128, no. 4, 1191-1196, 2000. MR 1705745 (2000i:53059)
  • 7. G. Perelman, Proof of the soul conjecture of Cheeger and Gromoll. J. Differential Geom. 40, no. 1, 209-212, 1994. MR 1285534 (95d:53037)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53C20, 53C22

Retrieve articles in all journals with MSC (2010): 53C20, 53C22


Additional Information

Jianming Wan
Affiliation: Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang, 310027, People’s Republic of China
Email: wanj_m@yahoo.com.cn

DOI: https://doi.org/10.1090/S0002-9939-2010-10549-X
Keywords: Closed geodesics, volume growth
Received by editor(s): February 25, 2010
Received by editor(s) in revised form: April 17, 2010
Published electronically: August 24, 2010
Communicated by: Jianguo Cao
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society