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Group actions and curvature. (English) Zbl 0271.53044


MSC:

53C20 Global Riemannian geometry, including pinching
57S15 Compact Lie groups of differentiable transformations
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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References:

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[2] Gromoll, D., Klingenberg, W., Meyer, W.: Riemannsche Geometrie im Großen. Lecture Notes in Mathematics55. Berlin-Heidelberg-New York: Springer 1968 · Zbl 0155.30701
[3] Grove, K., Karcher, H.: How to conjugateC 1-close group actions. Math. Z.132, 11-20 (1973) · Zbl 0254.57032 · doi:10.1007/BF01214029
[4] Grove, K., Karcher, H.: On pinched manifolds with fundamental groupZ 2. Compositio Math. to appear 1973 · Zbl 0266.53032
[5] Grove, K., Karcher, H., Ruh, E.: Group actions and Curvature. Bull. Amer. Math. Soc. to appear. · Zbl 0271.53044
[6] Hausner, M., Schwartz, J.T.: Lie groups; Lie algebras. New York: Gordon and Breach 1968 · Zbl 0192.35902
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[9] Kobayashi, S.: Topology of positively pinched Kähler manifolds. Tôhoku Math. J.15, 121-139 (1963) · Zbl 0114.37601 · doi:10.2748/tmj/1178243839
[10] Kobayashi, S., Ochiai, T.: Three-dimensional compact Kähler manifolds with positive holomorphic bisectional curvature. J. Math. Soc. Japan24, 465-480 (1972) · Zbl 0234.53051 · doi:10.2969/jmsj/02430465
[11] Lazard, M., Tits, J.: Domaines d’injectivité de l’application exponentielle. Topology4, 315-322 (1966) · Zbl 0156.03203 · doi:10.1016/0040-9383(66)90030-9
[12] Palais, R.S.: Equivalence of nearby differentiable actions of a group. Bull. Amer. Math. Soc.67, 362-364 (1961) · Zbl 0102.38101 · doi:10.1090/S0002-9904-1961-10617-4
[13] Ruh, E.A.: Curvature and differentiable structures on spheres. Comment. Math. Helv.46, 127-136 (1971) · Zbl 0206.50704 · doi:10.1007/BF02566833
[14] Ruh, E.A.: Krummung und differenzierbare Struktur auf Sphären, II. Math. Ann.205, 113-129 (1973) · Zbl 0273.53035 · doi:10.1007/BF01350841
[15] Shiohama, K.: Pinching theorem for the real projective space. To appear. · Zbl 0265.53043
[16] Sugimoto, M., Shiohama, K., Karcher, H.: On the differentiable pinching problem. Math. Ann.195, 1-16 (1971) · Zbl 0218.53063 · doi:10.1007/BF02059412
[17] Wolf, J.: Spaces of constant curvature. New York: McGraw-Hill 1967 · Zbl 0162.53304
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