Curvature homogeneous riemannian manifolds

F. Tricerri; L. Vanhecke

Annales scientifiques de l'École Normale Supérieure (1989)

  • Volume: 22, Issue: 4, page 535-554
  • ISSN: 0012-9593

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Tricerri, F., and Vanhecke, L.. "Curvature homogeneous riemannian manifolds." Annales scientifiques de l'École Normale Supérieure 22.4 (1989): 535-554. <http://eudml.org/doc/82261>.

@article{Tricerri1989,
author = {Tricerri, F., Vanhecke, L.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {symmetric space; curvature tensor; model space; nullity distribution; naturally reductive homogeneous Einstein space; isometry classes},
language = {eng},
number = {4},
pages = {535-554},
publisher = {Elsevier},
title = {Curvature homogeneous riemannian manifolds},
url = {http://eudml.org/doc/82261},
volume = {22},
year = {1989},
}

TY - JOUR
AU - Tricerri, F.
AU - Vanhecke, L.
TI - Curvature homogeneous riemannian manifolds
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1989
PB - Elsevier
VL - 22
IS - 4
SP - 535
EP - 554
LA - eng
KW - symmetric space; curvature tensor; model space; nullity distribution; naturally reductive homogeneous Einstein space; isometry classes
UR - http://eudml.org/doc/82261
ER -

References

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  1. [1] W. AMBROSE and I. M. SINGER, On Homogeneous Riemannian Manifolds (Duke Math. J., Vol. 25, 1958, pp. 657-669). Zbl0134.17802MR21 #1628
  2. [2] M. BERGER, L'œuvre d'André Lichnerowicz en géométrie riemannienne, in Physique quantique et géométrie, D. BERNARD and Y. CHOQUET-BRUHAT Eds. Colloque Géométrie et Physique 1986 en l'honneur de André Lichnerowicz, Travaux en cours, Hermann, Paris, 1988. Zbl0642.53002
  3. [3] A. L. BESSE, Einstein Manifolds, Springer-Verlag, Berlin, Heidelberg, New York, 1987. Zbl0613.53001MR88f:53087
  4. [4] J. E. D'ATRI and W. ZILLER, Naturally Reductive Metrics and Einstein Metrics on Compact Lie groups (Mem. Amer. Math. Soc., Vol. 215, 1979). Zbl0404.53044MR80i:53023
  5. [5] D. FERUS, H. KARCHER and H. F. MÜNZNER, Cliffordalgebren und neue Isoparametrische Hyperflöchen (Math. Z., Vol. 177, 1981, pp. 479-502). Zbl0443.53037
  6. [6] M. GROMOV, Structures métriques pour les variétés riemanniennes, Cedic, Paris, 1981. Zbl0509.53034MR85e:53051
  7. [7] S. HELGASON, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York, 1978. Zbl0451.53038MR80k:53081
  8. [8] S. KOBAYASHI and K. NOMIZU, Foundations of Differential Geometry, Vol. I and II, Interscience Publishers, New York, 1963, and 1969. Zbl0119.37502
  9. [9] O. KOWALSKI, Generalized Symmetric Spaces (Lecture Notes in Math., No. 805, Springer-Verlag, Berlin, Heidelberg, New York, 1980). Zbl0431.53042MR83d:53036
  10. [10] O. KOWALSKI and F. TRICERRI, Riemann Manifolds of Dimension n≦4 Admitting a Homogeneous Structure of Class F2 (Conferenze del Seminario di Matematica, Univ. Bari, Vol. 222, Laterza, Bari, 1987). Zbl0655.53038
  11. [11] O. KOWALSKI and L. VANHECKE, Riemann Manifolds with Homogeneous Geodesics, preprint. Zbl0692.53022
  12. [12] O. KOWALSKI, F. TRICERRI and L. VANHECKE, Curvature Homogeneous Riemannian Manifolds, in preparation. Zbl0836.53029
  13. [13] G. D. MOSTOW, Strong Rigidity of Locally Symmetric Spaces (Ann. of Math. Studies, Vol. 78, Princeton Univ. Press, 1973). Zbl0265.53039MR52 #5874
  14. [14] K. NOMIZU, Invariant Affine Connections on Homogeneous Spaces (Amer. J. Math., Vol. 76, 1954, pp. 33-65). Zbl0059.15805MR15,468f
  15. [15] K. SEKIGAWA, On the Riemannian Manifolds of the Form BxfF (Kōdai Math. Sem. Rep., Vol. 26, 1975, pp. 343-347). Zbl0304.53019MR55 #11171
  16. [16] J. SIMONS, On the Transitivity of Holonomy Systems (Ann. of Math., Vol. 76, 1962, pp. 213-234). Zbl0106.15201MR26 #5520
  17. [17] I. M. SINGER, Infinitesimally Homogeneous Spaces (Comm. Pure Appl. Math., Vol. 13, 1960, pp. 685-697). Zbl0171.42503MR24 #A1100
  18. [18] Z. I. SZABÓ, Structure Theorems on Riemannian Spaces Satisfying R (X, Y) . R = O. I. The local version (J. Differential Geometry, Vol. 17, 1982, pp. 531-582). Zbl0508.53025MR84e:53060
  19. [19] H. TAKAGI, On Curvature Homogeneity of Riemannian Manifolds (Tôhoku Math., J., Vol. 26, 1974, pp. 581-585). Zbl0302.53022MR51 #1669
  20. [20] F. TRICERRI and L. VANHECKE, Homogeneous Structures on Riemannian Manifolds (London Math. Soc. Lecture Note Series, Vol. 83, Cambridge Univ. Press, London, 1983). Zbl0509.53043MR85b:53052
  21. [21] F. TRICERRI and L. VANHECKE, Variétés riemanniennes dont le tenseur de courbure est celui d'un espace symétrique irréductible (C. R. Acad. Sci. Paris, T. 302, 1986, pp. 233-235). Zbl0585.53043MR87e:53072
  22. [22] M. Y. WANG and W. ZILLER, On Normal Homogeneous Einstien Manifolds (Ann. Scient. Éc. Norm. Sup., 4e série, Vol. 18, 1985, pp. 563-633). Zbl0598.53049MR87k:53113
  23. [23] J. WOLF, The Geometry and Structures of Isotropy Irreducible Homogeneous Spaces (Acta Math., Vol. 120, 1968, pp. 59-148); Correction (Acta Math., Vol. 152, 1984, pp. 141-142). Zbl0539.53037

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