Differentiable sphere theorem by curvature pinching

Yoshihiko SUYAMA

doi:10.2969/jmsj/04330527

Yoshihiko SUYAMA

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JOURNAL FREE ACCESS

1991 Volume 43 Issue 3 Pages 527-553

DOI https://doi.org/10.2969/jmsj/04330527

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Published: 1991 Received: July 24, 1989 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: SUBTITLE Details: Wrong : Dedicated to Professor Nobuyuki Ikeda on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. Berger, Les variétés riemanniennes (1/4)-pincées, Ann. Scuola Norm. Sup., Pisa, 14 (1960), 161-170.
2) D. Gromoll, Differenzierbare Strukturen und Metriken positiver Krümmung auf Sphären, Math. Ann., 164 (1966), 351-371.
3) K. Grove, H. Karcher and E.A. Ruh, Group actions and curvature, Invent. Math., 23 (1974), 31-48.
4) S. Helgason, Differential Geometry, Lie Group, and Symmetric Spaces, Academic Press, New York, 1978.
5) H.C. Im Hof and E.A. Ruh, An equivariant pinching theorem, Comment. Math. Helv., 50 (1975), 389-401.
6) W. Klingenberg, Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung, Comment. Math. Helv., 35 (1961), 47-54.
7) H. Omori, On the group of diffeomorphisms on a compact manifold, Global Analysis Symp. Pure Math., Berkeley, 15 (1968), 167-189.
8) E.A. Ruh, Curvature and differentiable structure on spheres, Comment. Math. Helv., 46 (1971), 127-136.
9) E.A. Ruh, Krummung und differentierbare Struktur auf Sphären, Comment. Math. Helv., 46 (1971), 127-136.
10) T. Sakai, On cut loci of compact symmetric spaces, Hokkaido Math. J., 6 (1977), 136-161.
11) Y. Shikata, On the differentiable pinching problem, Osaka Math. J., 4 (1967), 279-287.
12) M. Sugimoto and K. Shiohama, On the differentiable pinching problem, Math. Ann., 195 (1971), 1-16.

Right : [1] M. Berger, Les variétés riemanniennes (1/4)-pincées, Ann. Scuola Norm. Sup., Pisa, 14 (1960), 161-170.
[2] D. Gromoll, Differenzierbare Strukturen und Metriken positiver Krümmung auf Sphären, Math. Ann., 164 (1966), 351-371.
[3] K. Grove, H. Karcher and E. A. Ruh, Group actions and curvature, Invent. Math., 23 (1974), 31-48.
[4] S. Helgason, Differential Geometry, Lie Group, and Symmetric Spaces, Academic Press, New York, 1978.
[5] H. C. Im Hof and E. A. Ruh, An equivariant pinching theorem, Comment. Math. Helv., 50 (1975), 389-401.
[6] W. Klingenberg, Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung, Comment. Math. Helv., 35 (1961), 47-54.
[7] H. Omori, On the group of diffeomorphisms on a compact manifold, Global Analysis Symp. Pure Math., Berkeley, 15 (1968), 167-189.
[8] E. A. Ruh, Curvature and differentiable structure on spheres, Comment. Math. Helv., 46 (1971), 127-136.
[9] E. A. Ruh, Krummung und differentierbare Struktur auf Sphären, Comment. Math. Helv., 46 (1971), 127-136.
[10] T. Sakai, On cut loci of compact symmetric spaces, Hokkaido Math. J., 6 (1977), 136-161.
[11] Y. Shikata, On the differentiable pinching problem, Osaka Math. J., 4 (1967), 279-287.
[12] M. Sugimoto and K. Shiohama, On the differentiable pinching problem, Math. Ann., 195 (1971), 1-16.

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