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Volumn 3, Issue 2, 1990, Pages 355-374

On complete manifolds with nonnegative Ricci curvature

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EID: 84968508874     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0894-0347-1990-1030656-6     Document Type: Article
Times cited : (141)

References (27)
  • 1
    • 0000046378 scopus 로고
    • Lower curvature bounds, Toponogov’s Theorem, and bounded topology, I, II
    • U. Abresch, Lower curvature bounds, Toponogov’s Theorem, and bounded topology, I, II, Ann. Sci. Ecole Norm. Sup. (4) 18 (1985), 651–670
    • (1985) Ann. Sci. Ecole Norm. Sup. , vol.18 , Issue.4 , pp. 651-670
    • Abresch, U.1
  • 2
    • 0000066339 scopus 로고
    • Lower curvature bounds, Toponogov’s Theorem, and bounded topology, I, II
    • U. Abresch, Lower curvature bounds, Toponogov’s Theorem, and bounded topology, I, II, Ann. Sci. Ecole Norm. Sup. 20 (1987), 475–502.
    • (1987) Ann. Sci. Ecole Norm. Sup. , vol.20 , pp. 475-502
    • Abresch, U.1
  • 3
    • 84855677656 scopus 로고    scopus 로고
    • On the topology of complete manifolds of nonnegative Ricci curvature
    • (to appear)
    • M. T. Anderson, On the topology of complete manifolds of nonnegative Ricci curvature, Topology (to appear).
    • Topology
    • Anderson, M.T.1
  • 4
    • 84968518046 scopus 로고
    • An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures
    • S. Aloff and N. R. Wallach, An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures, Bull. Amer. Math. Soc. 81 (1975), 93–97.
    • (1975) Bull. Amer. Math. Soc , vol.81 , pp. 93-97
    • Aloff, S.1    Wallach, N.R.2
  • 5
    • 0000258452 scopus 로고
    • Quelques exemples des variétés riemanniennes complètes non compactes à courbure de Ricci positive
    • 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.
    • (1986) C. R. Acad. Sci. Paris Sér. , vol.1 , Issue.302 , pp. 159-161
    • Bergery, L.B.1
  • 8
    • 0001265427 scopus 로고
    • On the structure of complete manifolds of nonnegative curvature
    • J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96 (1972), 413–443.
    • (1972) Ann. of Math. , vol.96 , Issue.2 , pp. 413-443
    • Cheeger, J.1    Gromoll, D.2
  • 9
    • 84972500359 scopus 로고
    • The splitting theorem for manifolds of nonnegative Ricci curvature
    • ——, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geom. 6 (1971), 119–128.
    • (1971) J. Differential Geom. , vol.6 , pp. 119-128
    • Cheeger, J.1
  • 10
    • 84972535477 scopus 로고
    • Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
    • 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.
    • (1982) J. Differential Geom. , vol.17 , pp. 15-53
    • Cheeger, J.1    Gromov, M.2    Taylor, M.3
  • 11
    • 0039628706 scopus 로고
    • An elementary proof of the Cheeger-Gromoll splitting theorem
    • J. Eschenburg and E. Heintze, An elementary proof of the Cheeger-Gromoll splitting theorem, Ann. Global Anal. Geom. 2 (1984), 141–151.
    • (1984) Ann. Global Anal. Geom , vol.2 , pp. 141-151
    • Eschenburg, J.1    Heintze, E.2
  • 12
    • 0042936041 scopus 로고
    • A generalization of the Cheeger-Gromoll Splitting Theorem
    • G. Galloway, A generalization of the Cheeger-Gromoll Splitting Theorem, Arch. Math. 47 (1986), 372–375.
    • (1986) Arch. Math. , vol.47 , pp. 372-375
    • Galloway, G.1
  • 13
    • 0002305549 scopus 로고
    • On complete manifolds of positive curvature
    • D. Gromoll and W. T. Meyer, On complete manifolds of positive curvature, Ann. of Math. (2) 90 (1969), 75–90.
    • (1969) Ann. of Math. , vol.90 , Issue.2 , pp. 75-90
    • Gromoll, D.1    Meyer, W.T.2
  • 14
    • 84972536395 scopus 로고
    • Examples of complete manifolds with positive Ricci curvature
    • ——, Examples of complete manifolds with positive Ricci curvature, J. Differential Geom. 21 (1985), 195–211.
    • (1985) J. Differential Geom. , vol.21 , pp. 195-211
    • Gromoll, D.1
  • 15
    • 51249181993 scopus 로고
    • Curvature, diameter and Betti numbers
    • M. Gromov, Curvature, diameter and Betti numbers, Comment. Math. Helv. 56 (1981), 179–195.
    • (1981) Comment. Math. Helv. , vol.56 , pp. 179-195
    • Gromov, M.1
  • 17
    • 0003372262 scopus 로고
    • Metric differential geometry (Nordic Summer School 1985)
    • Springer-Verlag, Berlin and New York
    • K. Grove, Metric differential geometry (Nordic Summer School 1985), Lecture Notes in Math., vol. 1263, Springer-Verlag, Berlin and New York, 1987.
    • (1987) Lecture Notes in Math. , vol.1263
    • Grove, K.1
  • 18
    • 0001122135 scopus 로고
    • A generalized sphere theorem
    • K. Grove and K. Shiohama, A generalized sphere theorem, Ann. of Math. (2) 106 (1977), 201–211.
    • (1977) Ann. of Math. , vol.106 , Issue.2 , pp. 201-211
    • Grove, K.1    Shiohama, K.2
  • 19
    • 0007395589 scopus 로고
    • The unknottedness of minimal embeddings
    • H. B. Lawson, The unknottedness of minimal embeddings, Invent. Math. 11 (1970), 183–187.
    • (1970) Invent. Math. , vol.11 , pp. 183-187
    • Lawson, H.B.1
  • 20
    • 84972530010 scopus 로고
    • A note on curvature and fundamental group
    • J. Milnor, A note on curvature and fundamental group, J. Differential Geom. 2 (1968), 1–7.
    • (1968) J. Differential Geom. , vol.2 , pp. 1-7
    • Milnor, J.1
  • 21
    • 0004034109 scopus 로고
    • Asymptotic theory of finite dimensional normed spaces (Appendix: Isoperimetric inequalities in Riemannian manifolds, by M. Gromov)
    • Springer-Verlag, Berlin and New York
    • 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.
    • (1986) Lecture Notes in Math. , vol.1200
    • Milman, V.D.1    Schechtman, G.2
  • 22
    • 0001704354 scopus 로고
    • Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature
    • 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.
    • (1982) Ann. of Math. , vol.116 , pp. 621-659
    • Meeks, W.1    Simon, L.2    Yau, S.T.3
  • 23
    • 0003158595 scopus 로고
    • Examples of manifolds of positive Ricci-curvature
    • J. P. Sha and D. G. Yang, Examples of manifolds of positive Ricci-curvature, J. Differential Geom. 29 (1989), 95–103.
    • (1989) J. Differential Geom. , vol.29 , pp. 95-103
    • Sha, J.P.1    Yang, D.G.2
  • 25
    • 0001593830 scopus 로고
    • Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with nonnegative scalar curvature
    • 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.
    • (1979) Ann. of Math. , vol.110 , pp. 127-142
    • Schoen, R.1    Yau, S.T.2
  • 27
    • 0000567770 scopus 로고
    • Some function theoretic properties of complete Riemannian manifolds, and their applications to geometry
    • ——, Some function theoretic properties of complete Riemannian manifolds, and their applications to geometry, Indiana Univ. Math. J. 25 (1976), 659–670.
    • (1976) Indiana Univ. Math. J. , vol.25 , pp. 659-670
    • Yau, S.T.1


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