|
On the fundamental group of manifolds with almost nonnegative Ricci curvature
Author(s):
Seong-Hun
Paeng
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2577-2583.
MSC (2000):
Primary 53C20
Posted:
February 26, 2003
Retrieve article in:
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:
-
- [AC]
- M. T. Anderson, J. Cheeger,
 -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
 -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
Email:
shpaeng@kkucc.konkuk.ac.kr
DOI:
10.1090/S0002-9939-03-06885-0
PII:
S 0002-9939(03)06885-0
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
Posted:
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
Copyright of article:
Copyright
2003,
American Mathematical Society
|
Comments: webmaster@ams.org