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On the differentiable pinching problem. (English) Zbl 0214.48902

MSC:
53C20 Global Riemannian geometry, including pinching
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References:
[1] Berger, M.: An extension of Rauch’s metric comparison theorem and some applications. Illinois J. of Math.6, 700–712 (1962). · Zbl 0113.37003
[2] Gromoll, D.: Differenzierbare Strukturen und Metriken positiver Krümmung auf Sphären. Math. Ann.164, 353–371 (1966). · Zbl 0135.40301 · doi:10.1007/BF01350046
[3] —- Klingenberg, W., Meyer, W.: Riemannsche Geometrie im Großen. Berlin-Heidelberg-New York: Springer 1968. · Zbl 0155.30701
[4] Klingenberg, W.: Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung. Comment. Math. Helv.34, 35–54 (1961). · Zbl 0133.15005
[5] Rauch, H.: A contribution to differential geometry in the large. Ann. of Math.54, 38–55 (1951). · Zbl 0043.37202 · doi:10.2307/1969309
[6] Ruh, E.: Curvature and differentiable structures on spheres. Comment. Math. Helv.46, 127–136 (1971). · Zbl 0206.50704 · doi:10.1007/BF02566833
[7] Shikata, Y.: On the differentiable pinching problem. Osaka Math. J.4, 279–287 (1967). · Zbl 0155.31601
[8] Toponogov, V.A.: Riemannian spaces having their curvature bounded by a positive number. A.M.S. Transl.37, 291–336 (1964). · Zbl 0136.42904
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