×

zbMATH — the first resource for mathematics

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

MSC:
53C20 Global Riemannian geometry, including pinching
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
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 · minidml.mathdoc.fr
[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 · eudml:139466
[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 · eudml:162323
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.