|
Classification of almost quarter-pinched manifolds
Author(s):
Peter
Petersen;
Terence
Tao
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2437-2440.
MSC (2000):
Primary 53C21
Posted:
January 30, 2009
MathSciNet review:
2495279
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We show that if a simply connected manifold is almost quarter-pinched, then it is diffeomorphic to a CROSS or a sphere.
References:
-
- 1.
- U. Abresch and W.T. Meyer, Pinching below
, injectivity radius, and conjugate radius. J. Differential Geom. 40 (1994), no. 3, 643-691. MR 1305984 (95j:53053) - 2.
- U. Abresch and W.T. Meyer, A sphere theorem with a pinching constant below
. J. Differential Geom. 44 (1996), no. 2, 214-261. MR 1425576 (97i:53036) - 3.
- M. Berger, Sur les variétés riemanniennes pinc ées juste au-dessous de
. Ann. Inst. Fourier (Grenoble) 33 (1983), no. 2, 135-150. MR 699491 (85d:53017) - 4.
- C. Böhm and B. Wilking, Manifolds with positive curvature operators are space forms. Ann. of Math. (2) 167 (2008), 1079-1097.
- 5.
- S. Brendle and R. Schoen, Manifolds with
-pinched curvature are space forms. J. Amer. Math. Soc. 22 (2009), 287-307. - 6.
- S. Brendle and R. Schoen, Classification of manifolds with weakly
-pinched curvatures. Acta Math. 200 (2008), 1-13. MR 2386107 - 7.
- B. Chow and D. Knopf, The Ricci flow: An introduction.
Mathematical Surveys and Monographs, vol. 110, Amer. Math. Soc., Providence, RI, 2004. MR 2061425 (2005e:53101) - 8.
- B. Chow, P. Lu, and L. Ni, Hamilton's Ricci Flow.
Graduate Studies in Mathematics, vol. 77, Amer. Math. Soc., Providence, RI, 2006; Science Press, New York, 2006. MR 2274812 (2008a:53068) - 9.
- O. Durumeric, A generalization of Berger's theorem on almost
-pinched manifolds. II. J. Differential Geom. 26 (1987), no. 1, 101-139. MR 892033 (88m:53075) - 10.
- R. Hamilton, Three-manifolds with positive Ricci curvature.
J. Diff. Geom. 17 (1982), 255-306. MR 664497 (84a:53050) - 11.
- R. Hamilton, Four-manifolds with positive curvature operator.
J. Diff. Geom. 24 (1986), no. 2, 153-179. MR 862046 (87m:53055) - 12.
- R. Hamilton, The Formation of Singularities in the Ricci Flow.
Surveys in Differential Geometry, Vol. 2 (Cambridge, MA, 1993), Internat. Press, Cambridge, MA, 1995, 7-136. MR 1375255 (97e:53075) - 13.
- P. Petersen, Riemannian Geometry, second edition, Springer-Verlag, New York, 2006. MR 2243772 (2007a:53001)
- 14.
- P. Petersen and F. Wilhelm, An exotic sphere with positive sectional curvature, arXiv:math.DG/0805.0812
- 15.
- X. Rong, On the fundamental groups of manifolds of positive sectional curvature. Ann. of Math. (2) 143 (1996), no. 2, 397-411. MR 1381991 (97a:53067)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
53C21
Retrieve articles in all Journals with
MSC (2000):
53C21
Additional Information:
Peter
Petersen
Affiliation:
Department of Mathematics, University of California, 520 Portola Plaza, Los Angeles, California 90095
Email:
petersen@math.ucla.edu
Terence
Tao
Affiliation:
Department of Mathematics, University of California, 520 Portola Plaza, Los Angeles, California 90095
Email:
tao@math.ucla.edu
DOI:
10.1090/S0002-9939-09-09802-5
PII:
S 0002-9939(09)09802-5
Received by editor(s):
July 11, 2008,
Received by editor(s) in revised form:
October 16, 2008
Posted:
January 30, 2009
Communicated by:
Richard A. Wentworth
Copyright of article:
Copyright
2009,
American Mathematical Society
|