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Volumn 9, Issue 4, 1999, Pages 641-674

Positive pinching, volume and second Betti number

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EID: 0000997050     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000390050098     Document Type: Article
Times cited : (22)

References (47)
  • 1
    • 84972500238 scopus 로고
    • Pinching below 1/4, injectivity radius estimate, and sphere theorems
    • U. ABRESCH, W.T. MEYERS, Pinching below 1/4, injectivity radius estimate, and sphere theorems, J. Diff. Geom. 40 (1994), 643-691.
    • (1994) J. Diff. Geom. , vol.40 , pp. 643-691
    • Abresch, U.1    Meyers, W.T.2
  • 2
    • 84968518046 scopus 로고
    • An infinite family of 7-manifolds admitting positive curved Riemannian structures
    • S. ALOFF, N.R. WALLACH, An infinite family of 7-manifolds admitting positive 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
  • 6
    • 0008515703 scopus 로고
    • Exotic actions on spheres
    • Springer-Verlag, New Orleans, Berlin, New York
    • G. BREDON, Exotic actions on spheres, in "Proc. Conf. Transformations groups", Springer-Verlag, New Orleans, Berlin, New York (1968), 47-76.
    • (1968) Proc. Conf. Transformations Groups , pp. 47-76
    • Bredon, G.1
  • 9
    • 0001787207 scopus 로고
    • A.D. Alexandov spaces with curvature bounded below
    • Y. BURAGO, M. GROMOV, G. PEREL'MAN, A.D. Alexandov spaces with curvature bounded below, Uspekhi Mat. Nauk 47:2 (1992), 3-51.
    • (1992) Uspekhi Mat. Nauk , vol.47 , Issue.2 , pp. 3-51
    • Burago, Y.1    Gromov, M.2    Perel'man, G.3
  • 10
    • 0013127824 scopus 로고
    • On three-dimensional Riemannian spaces with curvature bounded above
    • Y. BURAGO, V.A. TOPONOGOV, On three-dimensional Riemannian spaces with curvature bounded above, Matematicheskie Zametki 13 (1973), 881-887.
    • (1973) Matematicheskie Zametki , vol.13 , pp. 881-887
    • Burago, Y.1    Toponogov, V.A.2
  • 11
    • 0002818931 scopus 로고
    • Finiteness theorems for Riemannian manifolds
    • J. CHEEGER, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61-75.
    • (1970) Amer. J. Math. , vol.92 , pp. 61-75
    • Cheeger, J.1
  • 12
    • 84968509403 scopus 로고
    • Nilpotent structures and invariant metrics on collapsed manifolds
    • J. CHEEGER, K. FUKAYA, M. GROMOV, Nilpotent structures and invariant metrics on collapsed manifolds, J. A.M.S. 5 (1992), 327-372.
    • (1992) J. A.M.S. , vol.5 , pp. 327-372
    • Cheeger, J.1    Fukaya, K.2    Gromov, M.3
  • 13
    • 84972496720 scopus 로고
    • On the lower bound for the injectivity radius of 1/4-pinched Riemannian manifolds
    • J. CHEEGER, D. GROMOLL, On the lower bound for the injectivity radius of 1/4-pinched Riemannian manifolds, J. Diff. Geom. 15 (1980), 437-442.
    • (1980) J. Diff. Geom. , vol.15 , pp. 437-442
    • Cheeger, J.1    Gromoll, D.2
  • 14
    • 84972538920 scopus 로고
    • Collapsing Riemannian manifolds while keeping their curvature bound I
    • J. CHEEGER, M. GROMOV, Collapsing Riemannian manifolds while keeping their curvature bound I, J. Diff. Geom. 23 (1986), 309-364.
    • (1986) J. Diff. Geom. , vol.23 , pp. 309-364
    • Cheeger, J.1    Gromov, M.2
  • 15
    • 84972508732 scopus 로고
    • Collapsing Riemannian manifolds while keeping their curvature bounded II
    • J. CHEEGER, M. GROMOV, Collapsing Riemannian manifolds while keeping their curvature bounded II, J. Diff. Geom. 32 (1990), 269-298.
    • (1990) J. Diff. Geom. , vol.32 , pp. 269-298
    • Cheeger, J.1    Gromov, M.2
  • 17
    • 0000720631 scopus 로고
    • New examples of manifolds with strictly positive curvature
    • J.-H. ESCHENBURG, New examples of manifolds with strictly positive curvature, Invent. Math. 66 (1982), 469-480.
    • (1982) Invent. Math. , vol.66 , pp. 469-480
    • Eschenburg, J.-H.1
  • 19
    • 0002639812 scopus 로고
    • Hausdorff convergence of Riemannian manifolds and its applications
    • (T. Ochiai, ed.), Kinokuniya, Tokyo
    • K. FUKAYA Hausdorff convergence of Riemannian manifolds and its applications, in "Recent Topics in Differential and Analytic Geometry" (T. Ochiai, ed.), Kinokuniya, Tokyo, 1990.
    • (1990) Recent Topics in Differential and Analytic Geometry
    • Fukaya, K.1
  • 20
    • 51249181993 scopus 로고
    • Curvature, diameter and Betti numbers
    • M. GROMOV, Curvature, diameter and Betti numbers, Commentarii Math. Helvetici 56 (1981), 179-195.
    • (1981) Commentarii Math. Helvetici , vol.56 , pp. 179-195
    • Gromov, M.1
  • 22
    • 38149147378 scopus 로고
    • Positively curved manifolds with maximal symmetry-rank
    • K. GROVE, C. SEARLE, Positively curved manifolds with maximal symmetry-rank, J. Pure Appl. Alg. 91 (1994), 137-142.
    • (1994) J. Pure Appl. Alg. , vol.91 , pp. 137-142
    • Grove, K.1    Searle, C.2
  • 24
    • 84972513449 scopus 로고
    • Three-manifolds with positive Ricci curvature
    • R. HAMILTON, Three-manifolds with positive Ricci curvature, J. Diff. Geom. 17 (1982), 255-306.
    • (1982) J. Diff. Geom. , vol.17 , pp. 255-306
    • Hamilton, R.1
  • 27
    • 0013127826 scopus 로고
    • Contributions to Riemannian geometry in the large
    • W. KLINGENBERG, Contributions to Riemannian geometry in the large, Ann. of Math. 69 (1959), 654-666.
    • (1959) Ann. of Math. , vol.69 , pp. 654-666
    • Klingenberg, W.1
  • 28
    • 51249195554 scopus 로고
    • Über mannigfaltigkeiten mit positiver krümmung
    • W. KLINGENBERG, Über Mannigfaltigkeiten mit positiver Krümmung, Comm. Math. Helv. 35 (1961), 47-54.
    • (1961) Comm. Math. Helv. , vol.35 , pp. 47-54
    • Klingenberg, W.1
  • 29
    • 0013075524 scopus 로고
    • Remarks on the injectivity radius estimate for almost 1/4-pinched manifolds
    • W. KLINGENBERG, T. SAKAI , Remarks on the injectivity radius estimate for almost 1/4-pinched manifolds, Springer Lecture Notes in Math. 1201 (1986), 156-164.
    • (1986) Springer Lecture Notes in Math. , vol.1201 , pp. 156-164
    • Klingenberg, W.1    Sakai, T.2
  • 31
    • 0040251483 scopus 로고
    • Some free actions of cyclic groups on spheres
    • J. MILNOR, Some Free Actions of Cyclic Groups on Spheres, Proc. Bombay Colloquium, 1964.
    • (1964) Proc. Bombay Colloquium
    • Milnor, J.1
  • 33
    • 0003320478 scopus 로고    scopus 로고
    • Riemannian geometry
    • Springer-Verlag, Berlin, Heidelberg, New York 171
    • P. PETERSEN, Riemannian Geometry, GTM 171, Springer-Verlag, Berlin, Heidelberg, New York 171, 1997.
    • (1997) GTM , vol.171
    • Petersen, P.1
  • 34
    • 0013075526 scopus 로고    scopus 로고
    • Collapsing vs. Positive pinching
    • this issue
    • A. PETRUNIN, X. RONG, W. TUSCHMANN, Collapsing vs. positive pinching, GAFA, this issue (1999), 699-735.
    • (1999) GAFA , pp. 699-735
    • Petrunin, A.1    Rong, X.2    Tuschmann, W.3
  • 35
    • 0039064926 scopus 로고    scopus 로고
    • Diffeomorphism finiteness, positive pinching, and second homotopy
    • this issue
    • A. PETRUNIN, W. TUSCHMANN, Diffeomorphism finiteness, positive pinching, and second homotopy, GAFA, this issue (1999), 736-774.
    • (1999) GAFA , pp. 736-774
    • Petrunin, A.1    Tuschmann, W.2
  • 37
    • 0030547161 scopus 로고    scopus 로고
    • On the fundamental groups of compact manifolds of positive sectional curvature
    • X. RONG, On the fundamental groups of compact manifolds of positive sectional curvature, Ann. of Math. 143 (1996), 397-411.
    • (1996) Ann. of Math. , vol.143 , pp. 397-411
    • Rong, X.1
  • 38
    • 0030507001 scopus 로고    scopus 로고
    • The almost cyclicity of the fundamental groups of positively curved manifolds
    • X. RONG, The almost cyclicity of the fundamental groups of positively curved manifolds, Invent. Math. 126 (1996), 47-64.
    • (1996) Invent. Math. , vol.126 , pp. 47-64
    • Rong, X.1
  • 39
    • 0039067573 scopus 로고    scopus 로고
    • Collapsed manifolds of pinched positive sectional curvature
    • to appear
    • X. RONG, Collapsed manifolds of pinched positive sectional curvature, J. Diff. Geom., to appear.
    • J. Diff. Geom.
    • Rong, X.1
  • 40
    • 0039659673 scopus 로고    scopus 로고
    • Positive curvature, local and global symmetry, and fundamental groups
    • to appear
    • X. RONG, Positive curvature, local and global symmetry, and fundamental groups, Amer. J. Math., to appear.
    • Amer. J. Math.
    • Rong, X.1
  • 41
    • 84973999286 scopus 로고
    • Bounding homotopy and homology groups by curvature and diameter
    • X. RONG, Bounding homotopy and homology groups by curvature and diameter, Duke Math. J. 78:2 (1995), 427-435.
    • (1995) Duke Math. J. , vol.78 , Issue.2 , pp. 427-435
    • Rong, X.1
  • 42
    • 0009245069 scopus 로고    scopus 로고
    • On the fundamental group of positively curved manifolds
    • K. SHANKAR, On the fundamental group of positively curved manifolds, J. Diff. Geom. 49 (1998), 179-182.
    • (1998) J. Diff. Geom. , vol.49 , pp. 179-182
    • Shankar, K.1
  • 45
    • 0003266356 scopus 로고
    • Elements of homotopy theory
    • Springer-Verlag, New York
    • G. WHITEHEAD, Elements of Homotopy Theory, GTM 61, Springer-Verlag, New York, 1978.
    • (1978) GTM , vol.61
    • Whitehead, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.