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)



On the fundamental group of manifolds with almost nonnegative Ricci curvature

Author: Seong-Hun Paeng
Journal: Proc. Amer. Math. Soc. 131 (2003), 2577-2583
MSC (2000): Primary 53C20
Published electronically: February 26, 2003
MathSciNet review: 1974658
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Gromov conjectured that the fundamental group of a manifold with almost nonnegative Ricci curvature is almost nilpotent. This conjecture is proved under the additional assumption on the conjugate radius. We show that there exists a nilpotent subgroup of finite index depending on a lower bound of the conjugate radius.

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

  • [AC] M. T. Anderson, J. Cheeger, $C^{\alpha }$-compactness for manifolds with Ricci curvature and injectivity radius bounded below, J. Diff. Geom. 35 (1992), 265-281. MR 93c:53028
  • [BK] P. Buser, H. Karcher, Gromov's almost flat manifolds, Astérisque, 1981. MR 83m:53070
  • [CC] J. Cheeger, T. B. Colding, Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann. Math. 144 (1996), 189-237. MR 97h:53038
  • [CG] J. Cheeger, D. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Diff. Geom. 6 (1971), 119-128. MR 46:2597
  • [CH] E. Calabi, P. Hartman, On the smoothness of isometries, Duke Math. J. 37 (1970), 741-750. MR 44:957
  • [F] K. Fukaya, Collapsing Riemannian manifolds to ones of lower dimensions, J. Diff. Geom. 25 (1987), 139-156. MR 88b:53050
  • [FY] K. Fukaya, T. Yamaguchi, The fundamental groups of almost nonnegatively curved manifolds, Ann. Math. 136 (1992), 253-333. MR 93h:53041
  • [G] M. Gromov, Almost flat manifolds, J. Diff. Geom. 13 (1978), 231-241. MR 80h:53041
  • [Pa] S.-H. Paeng, A generalized almost flat manifolds under a bounded $C^{0,\alpha }$-weak norm, Arch. Math. (Basel) 77 (2001), 423-429. MR 2002g:53050
  • [PWY] P. Petersen, G. Wei, R. Ye, Controlled geometry via smoothing, Comment. Math. Helv. 74 (1999), 345-363. MR 2000h:53040
  • [W] G. Wei, Ricci curvature and Betti number, J. Geom. Anal 7 (1997), 377-386. MR 2000d:53062

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53C20

Retrieve articles in all journals with MSC (2000): 53C20

Additional Information

Seong-Hun Paeng
Affiliation: Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-gu, Seoul 143-701, Korea

Keywords: Almost nilpotent group, almost nonnegative Ricci curvature
Received by editor(s): October 16, 2000
Received by editor(s) in revised form: August 23, 2001
Published electronically: February 26, 2003
Additional Notes: This work was partially supported by KIAS and by grant No.1999-2-102-002-3 from the interdisciplinary research program of the KOSEF
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society