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Bourguignon, Jean-Pierre; Karcher, Hermann

Curvature operators: Pinching estimates and geometric examples. (English) Zbl 0386.53031

Ann. Sci. Éc. Norm. Supér. (4) 11, No. 1, 71-92 (1978).
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Cited in 3 Reviews
Cited in 54 Documents

MSC:

53C20 Global Riemannian geometry, including pinching
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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References:

[1] A. BESSE , Manifolds all of whose Geodesics are Closed , Erg. der Math., Springer, 1978 . MR 80c:53044 | Zbl 0387.53010 · Zbl 0387.53010
[2] J. P. BOURGUIGNON , Sur les formes harmoniques du type de la courbure (C. R. Acad. Sc., Paris, t. 286, 1978 , pp. 337-341). MR 57 #13782 | Zbl 0374.53019 · Zbl 0374.53019
[3] E. CALABI et E. VESENTINI , On Compact Locally Symmetric Kähler Manifolds (Ann. of Math., Vol. 71, 1960 , pp. 472-507). MR 22 #1922b | Zbl 0100.36002 · Zbl 0100.36002 · doi:10.2307/1969939
[4] S. GALLOT et D. MEYER , Opérateur de courbure et laplacien des formes différentielles d’une variété riemannienne (J. Math. pures et appl., T. 54, 1975 , pp. 259-284). MR 56 #13128 | Zbl 0316.53036 · Zbl 0316.53036
[5] R. GEROCH , Positive Sectional Curvature does not Imply Positive Gauss-Bonnet Integrand (Proc. A.M.S., Vol. 54, 1976 , pp. 267-270). MR 52 #11784 | Zbl 0325.53042 · Zbl 0325.53042 · doi:10.2307/2040798
[6] S. HELGASON , Differential Geometry and Symmetric Spaces , Academic Press, 1962 . MR 26 #2986 | Zbl 0111.18101 · Zbl 0111.18101
[7] G. JENSEN , Embeddings of Stiefel Manifolds into Grassmannians (Duke Math. J., Vol. 42, 1975 , pp. 397-407). Article | MR 51 #11360 | Zbl 0335.53042 · Zbl 0335.53042 · doi:10.1215/S0012-7094-75-04238-6
[8] H. KARCHER , Pinching implies Strong Pinching (Comment. Math. Helv., Vol. 46, 1971 , pp. 124-126). MR 45 #1076 | Zbl 0216.43803 · Zbl 0216.43803 · doi:10.1007/BF02566832
[9] T. KATO , Perturbation Theory for Linear Operators , Grund. der math. Wiss., Springer, 1966 . MR 34 #3324 | Zbl 0148.12601 · Zbl 0148.12601
[10] P. KLEMBECK , On Geroch’s Counterexample to the Algebraic Hopf Conjecture (Proc. A.M.S., Vol. 59, 1976 , pp. 334-336). MR 55 #1250 | Zbl 0341.53011 · Zbl 0341.53011 · doi:10.2307/2041496
[11] N. KOISO , Critical Metrics and Non-Deformability of Certain Riemannian Structures (Preprint, 1977 ).
[12] R. S. KULKARNI , On the Bianchi Identities (Math. Ann., Vol. 199, 1972 , pp. 175-204). MR 49 #3767 | Zbl 0234.53021 · Zbl 0234.53021 · doi:10.1007/BF01429873
[13] H. MAILLOT , Sur l’opérateur de courbure d’une variété riemannienne (Thèse de 3e cycle, Université Claude-Bernard, Lyon, 1974 ).
[14] A. POLOMBO , Nombres caractéristiques d’une variété riemannienne (Thèse de 3e cycle, Université Paris-VII, 1976 ).
[15] S. STERNBERG , Lectures on Differential Geometry , Prentice Hall, 1964 . MR 33 #1797 | Zbl 0129.13102 · Zbl 0129.13102
[16] H. WEYL , Classical Groups , Princeton University Press, Princeton, 1939 . JFM 65.0058.02 · JFM 65.0058.02
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