Journal of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6834(e) ISSN 0894-0347(p)

On complete manifolds with nonnegative Ricci curvature

Author(s): Uwe Abresch; Detlef Gromoll
Journal: J. Amer. Math. Soc. 3 (1990), 355-374.
MSC: Primary 53C21
MathSciNet review: 1030656
Retrieve article in: PDF
This article is available free of charge

References:

[A]: U. Abresch, Lower curvature bounds, Toponogov's Theorem, and bounded topology, I, II, Ann. Sci. Ecole Norm. Sup. (4) 18 (1985), 651-670 and 20 (1987), 475-502. MR 839689 (87j:53058)
[An]: M. T. Anderson, On the topology of complete manifolds of nonnegative Ricci curvature, Topology (to appear). MR 1046624 (91b:53041)
[AW]: S. Aloff and N. R. Wallach, An infinite family of distinct -manifolds admitting positively curved Riemannian structures, Bull. Amer. Math. Soc. 81 (1975), 93-97. MR 0370624 (51:6851)
[BB]: L. Bérard Bergery, Quelques exemples des variétés riemanniennes complètes non compactes à courbure de Ricci positive, C. R. Acad. Sci. Paris Sér. I 302 (1986), 159-161. MR 832061 (87g:53058)
[BC]: R. Bishop and R. Crittenden, Geometry of manifolds, Academic Press, New York, 1964. MR 0169148 (29:6401)
[CE]: J. Cheeger and D. Ebin, Comparison theorems in Riemannian geometry, North-Holland, New York, 1975. MR 0458335 (56:16538)
[CG1]: J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96 (1972), 413-443. MR 0309010 (46:8121)
[CG2]: -, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geom. 6 (1971), 119-128. MR 0303460 (46:2597)
[CGT]: J. Cheeger, M. Gromov, and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982), 15-53. MR 658471 (84b:58109)
[EH]: J. Eschenburg and E. Heintze, An elementary proof of the Cheeger-Gromoll splitting theorem, Ann. Global Anal. Geom. 2 (1984), 141-151. MR 777905 (86h:53042)
[Ga1]: G. Galloway, A generalization of the Cheeger-Gromoll Splitting Theorem, Arch. Math. 47 (1986), 372-375. MR 866527 (88a:53031)
[GM1]: D. Gromoll and W. T. Meyer, On complete manifolds of positive curvature, Ann. of Math. (2) 90 (1969), 75-90.
[GM2]: -, Examples of complete manifolds with positive Ricci curvature, J. Differential Geom. 21 (1985), 195-211. MR 816669 (87b:53068)
[G]: M. Gromov, Curvature, diameter and Betti numbers, Comment. Math. Helv. 56 (1981), 179-195. MR 630949 (82k:53062)
[GLP]: M. Gromov, J. Lafontaine, and P. Pansu, Structures métriques pour les variétés Riemanniennes, Nathan, Paris, 1982.
[Gr]: K. Grove, Metric differential geometry (Nordic Summer School 1985), Lecture Notes in Math., vol. 1263, Springer-Verlag, Berlin and New York, 1987. MR 905882 (88i:53075)
[GS]: K. Grove and K. Shiohama, A generalized sphere theorem, Ann. of Math. (2) 106 (1977), 201-211. MR 0500705 (58:18268)
[L]: H. B. Lawson, The unknottedness of minimal embeddings, Invent. Math. 11 (1970), 183-187. MR 0287447 (44:4651)
[M]: J. Milnor, A note on curvature and fundamental group, J. Differential Geom. 2 (1968), 1-7. MR 0232311 (38:636)
[MS]: V. D. Milman and G. Schechtman, Asymptotic theory of finite dimensional normed spaces (Appendix: Isoperimetric inequalities in Riemannian manifolds, by M. Gromov), Lecture Notes in Math., vol. 1200, Springer-Verlag, Berlin and New York, 1986. MR 856576 (87m:46038)
[MSY]: W. Meeks III, L. Simon, and S. T. Yau, Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature, Ann. of Math. 116 (1982), 621-659. MR 678484 (84f:53053)
[ShY]: J. P. Sha and D. G. Yang, Examples of manifolds of positive Ricci-curvature, J. Differential Geom. 29 (1989), 95-103. MR 978078 (90c:53110)
[ShY1]: -, Positive Ricci curvature on the connected sums of ${S^n} \times {S^m}$ , J. Differential Geom. (to appear).
[SY]: R. Schoen and S. T. Yau, Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with nonnegative scalar curvature, Ann. of Math. 110 (1979), 127-142. MR 541332 (81k:58029)
[Y1]: S. T. Yau, Seminar on differential geometry, Princeton Univ. Press, Princeton, NJ, 1982. MR 645728 (83a:53002)
[Y2]: -, Some function theoretic properties of complete Riemannian manifolds, and their applications to geometry, Indiana Univ. Math. J. 25 (1976), 659-670. MR 0417452 (54:5502)

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|