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References
S. Bando, On the classification of three-dimensional compact Kaehler manifolds of nonnegative bisectional curvature, J. Differential Geometry, 19(1984), 283–297.
S. Bando, Curvature operators and eigenvalue problems, informal notes (in Japanese).
M. Berger, Sur les variétés à opérateur de courbure positif, Comptes rendus, 253(1961), 2832–2834.
J.P. Bourguignon and H. Karcher, Curvature operators: pinching estimates and geometric examples, Ann. Sci. Ec. Norm. Sup., 11 (1978), 71–92.
D.M. Deturck, Deforming metrics in the direction of their Ricci tensors, J. Differential Geometry, 18(1983), 157–162.
R.S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc., 7(1982), 65–222.
R.S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry, 17(1982), 255–306.
R.S. Hamilton, Four-manifolds with positive curvature operator, preprint.
G. Huisken, Ricci deformation of the metric on a Riemannian manifold, preprint.
T. Kashiwada, On the curvature operator of second kind, preprint.
N. Koiso, On the second derivative of the total scalar curvature, Osaka J. Math., 16(1979), 413–421.
C. Margerin, Some results about the positive curvature operators and point-wise δ (n)-pinched manifolds, informal notes.
D. Meyer, Sur les variétés riemanniennes à opérateur de courbure positif, Comptes rendus, 272(1971), 482–485.
Y. Muto, On Einstein metrics, J. Differential Geometry, 9(1974), 521–530.
S. Nishikawa, Deformation of Riemannian metrics and manifolds with bounded curvature ratios, to appear in Proc. Symp. Pure Math., 1985.
K. Ogiue and S. Tachibana, Les variétés riemanniennes dont l'opérateur de courbure restreint est positif sont des sphères d'homologie réelle, Comptes rendus, 289(1979), 29–30.
E.A. Ruh, Riemannian manifolds with bounded curvature ratios, J. Differential Geometry, 17(1982), 643–653.
Y.T. Siu, Complex-analyticity of harmonic maps, vanishing and Lefschetz theorems, J. Differential Geometry, 17(1982), 55–138.
S. Tachibana, A theorem on Riemannian manifolds of positive curvature operator, Proc. Japan Acad., 50(1974), 301–302.
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© 1986 Springer-Verlag
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Nishikawa, S. (1986). On deformation of Riemannian metrics and manifolds with positive curvature operator. In: Shiohama, K., Sakai, T., Sunada, T. (eds) Curvature and Topology of Riemannian Manifolds. Lecture Notes in Mathematics, vol 1201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075657
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DOI: https://doi.org/10.1007/BFb0075657
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