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Bérard Bergery, Lionel

Sur la courbure des métriques riemanniennes invariantes des groupes de Lie et des espaces homogènes. (French) Zbl 0426.53038

Ann. Sci. Éc. Norm. Supér. (4) 11, No. 4, 543-576 (1978).
Reviewer: Valentin Boju (Montreal)
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0426.53038

Cited in 1 Review
Cited in 25 Documents

MSC:

53C30 Differential geometry of homogeneous manifolds
53C20 Global Riemannian geometry, including pinching
22E99 Lie groups

Keywords:

G-invariant Riemannian metric; sectional curvature; Ricci curvature

Citations:

Zbl 0341.53030
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Full Text: DOI Numdam EuDML

References:

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[2] D. V. ALEKSEEVSKI et B. N. KIMEL’FEL’D , Structure of Homogeneous Riemann Spaces with zero Ricci Curvature (Funct. Analysis and Appl., vol. 9, 1975 , p. 97-102). Zbl 0316.53041 · Zbl 0316.53041 · doi:10.1007/BF01075445
[3] L. BÉRARD BERGERY , 1, Sur certaines fibrations d’espaces homogènes riemanniens (Compositio Mathematica, vol. 30, 1975 , p. 43-61) ; 2, Les variétés riemanniennes homogènes simplement connexe de dimension impaire à courbure strictement positive (J. Math. pures et appl., vol. 55, 1976 , p. 47-68). MR 51 #6659 | Zbl 0289.53037 · Zbl 0289.53037
[4] M. BERGER , Les variétés riemanniennes homogènes normales simplement connexes à courbure strictement positive (Annali della Scuola Norm. Sup. Pisa, vol. 15, 1961 , p. 179-246). Numdam | MR 24 #A2919 | Zbl 0101.14201 · Zbl 0101.14201
[5] A. BESSE , Manifolds all of whose Geodesics are closed (Ergebnisse des Mathematik n^\circ 93, Springer Verlag, 1978 ). MR 80c:53044 | Zbl 0387.53010 · Zbl 0387.53010
[6] N. BOURBAKI , Groupes et algèbres de Lie , chap. 1, Hermann, 1971 . · Zbl 0213.04103
[7] J. CHEEGER et D. G. EBIN , Comparison theorems in Riemannian Geometry , North-Holland, 1975 . MR 56 #16538 | Zbl 0309.53035 · Zbl 0309.53035
[8] J. CHEEGER et D. GROMOLL . The Splitting Theorem for Manifolds of nonnegative Ricci Curvature J. of diff. geom. vol. 6, 1971 , p. 119-128). MR 46 #2597 | Zbl 0223.53033 · Zbl 0223.53033
[9] J. I. HANO , On Kaehlerian Homogeneous Spaces of Unimodular Lie Groups (Amer. J. of Math., vol. 79, 1957 , p. 885-900). MR 20 #2477 | Zbl 0096.16203 · Zbl 0096.16203 · doi:10.2307/2372440
[10] E. HEINTZE , Riemannsche Solvmannigfaltigkeiten (Geom. Dedicata, 1, 1972 , p. 141-147). MR 46 #8123 | Zbl 0249.53041 · Zbl 0249.53041 · doi:10.1007/BF00147515
[11] S. HELGASON , Differential Geometry and Symmetric Spaces , Academic Press, 1962 . MR 26 #2986 | Zbl 0111.18101 · Zbl 0111.18101
[12] G. HOCHSCHILD , The Structure of Lie groups , Holden-Day, 1965 . MR 34 #7696 | Zbl 0131.02702 · Zbl 0131.02702
[13] G. R. JENSEN , The scalar curvature of left-invariant Riemannian metrics (Indiana Univ. Math. J, vol. 20, 1971 , p. 1125-1143). MR 44 #6914 | Zbl 0219.53044 · Zbl 0219.53044 · doi:10.1512/iumj.1971.20.20104
[14] S. KOBAYASHI et K. NOMIZU , Foundations of Differential Geometry (Interscience Publishers, vol. I, 1963 , II, 1969 ). Zbl 0119.37502 · Zbl 0119.37502
[15] J. MILNOR , Curvatures of Left Invariant Metrics on Lie Groups (Adv. in Math., vol. 21, 1976 , p. 293-329). MR 54 #12970 | Zbl 0341.53030 · Zbl 0341.53030 · doi:10.1016/S0001-8708(76)80002-3
[16] B. O’NEILL , The Fundamental Equations of a Submersion (Mich. Math. J., 13, 1966 , p. 459-469). Article | MR 34 #751 | Zbl 0145.18602 · Zbl 0145.18602 · doi:10.1307/mmj/1028999604
[17] J. TITS , Tabellen zu den einfachen Lie Gruppen und ihren Darstellungen (Lecture Notes, 40, Springer Verlag 1967 ). MR 36 #1575 | Zbl 0166.29703 · Zbl 0166.29703 · doi:10.1007/BFb0080324
[18] N. WALLACH , Compact Homogeneous Riemannian Manifolds with Strictly Positive Curvature (Ann. of Math., vol. 96, 1972 , p. 277-295). MR 46 #6243 | Zbl 0261.53033 · Zbl 0261.53033 · doi:10.2307/1970789
[19] J. A. WOLF , The Geometry and Structure of Isotropy Irreducible Homogeneous Spaces (Acta Math., vol. 120, 1968 , p. 59-148). MR 36 #6549 | Zbl 0157.52102 · Zbl 0157.52102 · doi:10.1007/BF02394607
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