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A generalization of the classical sphere theorem
Author(s):
Changyu
Xia
Journal:
Proc. Amer. Math. Soc.
125
(1997),
255-258.
MSC (1991):
Primary 53C20
MathSciNet review:
1363441
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Abstract:
In this paper, we prove a sphere theorem for Riemannian manifolds with partially positive curvature which generalizes the classical sphere theorem.
References:
- 1.
- J. Cheeger and D. Ebin, Comparison Theorems in Riemannian Geometry, North-holland, New-York, 1975.
- 2.
- K. Grove and K. Shiohama, A generalized sphere theorem, Ann. of Math., 106 (1977), 201-211. MR 58:18268
- 3.
- R. Hamilton, Three manifolds with positive Ricci curvature, J. Differential Geom., 17 (1982), 255-306. MR 84a:53050
- 4.
- P. Hartman, Oscillation criteria for self-adjoint second-order differential systems and `` principal sectional curvature " , J. Differential Equations 34 (1979), 326-338. MR 81a:34034
- 5.
- W. Klingenberg, Riemannian Geometry, Berlin, New York : de Gruyter, 1982. MR 84j:53001
- 6.
- H. Wu, Manifolds of partially positive curvature, Indiana Univ. Math. J., 36 (1987), 525-548. MR 88k:53068
- 7.
- C.Y. Xia, Rigidity and sphere theorem for manifolds with positive Ricci curvature, manuscripta math., 85 (1994), 79-87. MR 95j:53057
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Additional Information:
Changyu
Xia
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
Address at time of publication:
Instituto de Matemática Pure e Aplicada, Estrada Dona Castorina, 110, 22460-320 Rio de Janeiro RJ, Brasil
Email:
xiacy@impa.br
DOI:
10.1090/S0002-9939-97-03721-0
PII:
S 0002-9939(97)03721-0
Keywords:
Curvature,
sphere theorem
Received by editor(s):
August 2, 1995
Additional Notes:
This work was partially supported by the JSPS postdoctoral fellowship and National Natural Science Foundation of China.
Communicated by:
Christopher Croke
Copyright of article:
Copyright
1997,
American Mathematical Society
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