A pinching problem for locally homogeneous spaces

Atsushi KATSUDA

doi:10.2969/jmsj/04110057

Atsushi KATSUDA

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JOURNAL FREE ACCESS

1989 Volume 41 Issue 1 Pages 57-74

DOI https://doi.org/10.2969/jmsj/04110057

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Published: 1989 Received: May 13, 1985 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) W. Ambrose and I. M. Singer, On homogeneous Riemannian manifolds, Duke Math. J., 25 (1958), 647-669.
2) M. Berger, Sur les variétés riemannienes pincées juste audessous de 1/4, Ann. Inst. Fourier, 33 (1983), 135-150.
3) J. Cheeger, Comparison and finiteness theorems for Riemannian manifolds, Ph. D. Thesis, Princeton Univ., 1967.
4) J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math., 92 (1970), 61-74.
5) J. Cheeger and D. G. Ebin, Comparison Theorems in Riemannian Geometry, American Elsevier, Now York, 1975.
6) K. Fukaya, Theory of convergence for Riemannian orbifolds, Japan J. Math., 12 (1986), 121-160.
7) R. E. Greene and H. Wu, Lipshitz convergence of Riemannian manifolds, Pacific J. Math., 131 (1988), 119-141.
8) M. Gromov, Manifolds of negative curvature, J. Diff. Geom., 13 (1978), 223-230.
9) M. Gromov, Structures métriques pour les variétés riemanniennes, rédigé par J. Lafontaine et P. Pansu, Cedic/Fernand Nathan, 1981.
10) R. Hamilton, Three manifolds with positive Ricci curvature, J. Diff. Geom., 17 (1982), 255-306.
11) A. Katsuda, Gromov's convergence theorem and its application, Nagoya Math. J., 100 (1985), 11-48.
12) S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, John Wiley, New York, I, 1963, II, 1969.
13) Min-Oo and E. Ruh, Comparison theorems for compact symmetric spaces, Ann. Sci. École Norm. Sup., 12 (1979), 335-353.
14) Min-Oo and E. Ruh, Vanishing theorems and almost symmetric spaces of noncompact type, Math. Ann., 257 (1981), 419-433.
15) D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience, 1955.
16) T. Sakai, Comparison and finiteness theorems in Riemannian geometry, Adv. Stud. Pure Math., 3, Geometry of Geodesics, pp. 125-181.
17) F. Tricerri and L. Vanhecke, Homogeneous Structures on Riemannian Manifolds, London Math. Soc., Lecture Note Ser., 83, Cambridge Univ. Press, 1983.
18) S. Peters, Convergence of Riemannian manifolds, Compositio Math., 62 (1987), 3-16.

Right : [1] W. Ambrose and I. M. Singer, On homogeneous Riemannian manifolds, Duke Math. J., 25 (1958), 647-669.
[2] M. Berger, Sur les variétés riemannienes pincées juste audessous de 1/4, Ann. Inst. Fourier, 33 (1983), 135-150.
[3] J. Cheeger, Comparison and finiteness theorems for Riemannian manifolds, Ph. D. Thesis, Princeton Univ., 1967.
[4] J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math., 92 (1970), 61-74.
[5] J. Cheeger and D. G. Ebin, Comparison Theorems in Riemannian Geometry, American Elsevier, Now York, 1975.
[6] K. Fukaya, Theory of convergence for Riemannian orbifolds, Japan J. Math., 12 (1986), 121-160.
[7] R. E. Greene and H. Wu, Lipshitz convergence of Riemannian manifolds, Pacific J. Math., 131 (1988), 119-141.
[8] M. Gromov, Manifolds of negative curvature, J. Diff. Geom., 13 (1978), 223-230.
[9] M. Gromov, Structures métriques pour les variétés riemanniennes, rédigé par J. Lafontaine et P. Pansu, Cedic/Fernand Nathan, 1981.
[10] R. Hamilton, Three manifolds with positive Ricci curvature, J. Diff. Geom., 17 (1982), 255-306.
[11] A. Katsuda, Gromov's convergence theorem and its application, Nagoya Math. J., 100 (1985), 11-48.
[12] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, John Wiley, New York, I, 1963, II, 1969.
[13] Min-Oo and E. Ruh, Comparison theorems for compact symmetric spaces, Ann. Sci. École Norm. Sup., 12 (1979), 335-353.
[14] Min-Oo and E. Ruh, Vanishing theorems and almost symmetric spaces of noncompact type, Math. Ann., 257 (1981), 419-433.
[15] D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience, 1955.
[16] T. Sakai, Comparison and finiteness theorems in Riemannian geometry, Adv. Stud. Pure Math., 3, Geometry of Geodesics, pp. 125-181.
[17] F. Tricerri and L. Vanhecke, Homogeneous Structures on Riemannian Manifolds, London Math. Soc., Lecture Note Ser., 83, Cambridge Univ. Press, 1983.
[18] S. Peters, Convergence of Riemannian manifolds, Compositio Math., 62 (1987), 3-16.

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