A pinching problem for symmetric spaces of rank one

Takao YAMAGUCHI

doi:10.2969/jmsj/03630419

Takao YAMAGUCHI

著者情報

ジャーナルフリー

1984 年 36 巻 3 号 p. 419-431

DOI https://doi.org/10.2969/jmsj/03630419

詳細

Published: 1984 Received: 1983/06/27 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) M. Berger, Les variétés riemanniennes (1/4) -pincées, Ann. Scuola Norm. Sup. Pisa, 14 (1960), 161-170.
2) J. Cheeger, Comparison and finiteness theorems for Riemannian manifolds, Ph. D. Thesis, Princeton Univ., 1967.
3) J. Cheeger, Pinching theorems for a certain class of Riemannian manifolds, Amer. J. Math., 91 (1969), 807-834.
4) J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math., 92 (1970), 61-74.
5) J. Cheeger and D. Ebin, Comparison theorems in Riemannian geometry, North-Holland, 1975.
6) D. Gromoll, Differenzierbare Strukturen und Metriken positiver Krümmung auf Sphären, Math. Ann., 164 (1966), 353-371.
7) M. Gromov, Structures métriques pour les variétés riemanniennes, régigé parJ. Lafontaine et P. Pansu, Cedic-Fernand Nathan, Paris, 1981.
8) K. Grove and K. Shiohama, A generalized sphere theorem, Ann. of Math., 106 (1977), 201-211.
9) W. Klingenberg, Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung, Comment. Math. Helv., 35 (1961), 47-54.
10) Oo-Min and E. Ruh, Comparison theorems for compact symmetric spaces, Ann. Sci. École Norm. Sup., 12 (1979), 335-353.
11) S. Peters, Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds, preprint, 1983.
12) H. Rauch, A contribution to differential geometry in the large, Ann. of Math., 54 (1951), 38-55.
13) T. Sakai, On the diameter of some riemannian manifolds, Arch. Math., 30 (1978) 427-434.
14) Y. Shikata, On the differentiable pinching problem, Osaka J. Math., 4 (1967), 279-283.
15) K. Shiohama, A sphere theorem for manifolds of positive Ricci curvature, Trans. Amer. Math. Soc., 275 (1983), 811-819.
16) M. Sugimoto and K. Shiohama, On the differentiable pinching problem, Math. Ann., 195 (1971), 1-16.
17) T. Yamaguchi, On the number of diffeomorphism classes in a certain class of Riemannian manifolds, to appear in Nagoya Math. J.
18) T. Yamaguchi, A differentiable sphere theorem for volume-pinched manifolds, to appear in Geometry of geodesics and related topics, Advanced Studies in Pure Math., 3, Kinokuniya, Tokyo.

Right : [1] M. Berger, Les variétés riemanniennes (1/4)-pincées, Ann. Scuola Norm. Sup. Pisa, 14 (1960), 161-170.
[2] J. Cheeger, Comparison and finiteness theorems for Riemannian manifolds, Ph. D. Thesis, Princeton Univ., 1967.
[3] J. Cheeger, Pinching theorems for a certain class of Riemannian manifolds, Amer. J. Math., 91 (1969), 807-834.
[4] J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math., 92 (1970), 61-74.
[5] J. Cheeger and D. Ebin, Comparison theorems in Riemannian geometry, North-Holland, 1975.
[6] D. Gromoll, Differenzierbare Strukturen und Metriken positiver Krümmung auf Sphären, Math. Ann., 164 (1966), 353-371.
[7] M. Gromov, Structures métriques pour les variétés riemanniennes, régigé parJ. Lafontaine et P. Pansu, Cedic-Fernand Nathan, Paris, 1981.
[8] K. Grove and K. Shiohama, A generalized sphere theorem, Ann. of Math., 106 (1977), 201-211.
[9] W. Klingenberg, Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung, Comment. Math. Helv., 35 (1961), 47-54.
[10] Oo-Min and E. Ruh, Comparison theorems for compact symmetric spaces, Ann. Sci. École Norm. Sup., 12 (1979), 335-353.
[11] S. Peters, Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds, preprint, 1983.
[12] H. Rauch, A contribution to differential geometry in the large, Ann. of Math., 54 (1951), 38-55.
[13] T. Sakai, On the diameter of some riemannian manifolds, Arch. Math., 30 (1978) 427-434.
[14] Y. Shikata, On the differentiable pinching problem, Osaka J. Math., 4 (1967), 279-283.
[15] K. Shiohama, A sphere theorem for manifolds of positive Ricci curvature, Trans. Amer. Math. Soc., 275 (1983), 811-819.
[16] M. Sugimoto and K. Shiohama, On the differentiable pinching problem, Math. Ann., 195 (1971), 1-16.
[17] T. Yamaguchi, On the number of diffeomorphism classes in a certain class of Riemannian manifolds, to appear in Nagoya Math. J.
[18] T. Yamaguchi, A differentiable sphere theorem for volume-pinched manifolds, to appear in Geometry of geodesics and related topics, Advanced Studies in Pure Math., 3, Kinokuniya, Tokyo.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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