Four-dimensional curvature homogeneous spaces

Kouei Sekigawa; Hiroshi Suga; Lieven Vanhecke

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 2, page 261-268
  • ISSN: 0010-2628

Abstract

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We prove that a four-dimensional, connected, simply connected and complete Riemannian manifold which is curvature homogeneous up to order two is a homogeneous Riemannian space.

How to cite

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Sekigawa, Kouei, Suga, Hiroshi, and Vanhecke, Lieven. "Four-dimensional curvature homogeneous spaces." Commentationes Mathematicae Universitatis Carolinae 33.2 (1992): 261-268. <http://eudml.org/doc/247378>.

@article{Sekigawa1992,
abstract = {We prove that a four-dimensional, connected, simply connected and complete Riemannian manifold which is curvature homogeneous up to order two is a homogeneous Riemannian space.},
author = {Sekigawa, Kouei, Suga, Hiroshi, Vanhecke, Lieven},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Riemannian manifold; curvature homogeneous spaces; homogeneous spaces; locally homogeneous space; Singer's estimate},
language = {eng},
number = {2},
pages = {261-268},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Four-dimensional curvature homogeneous spaces},
url = {http://eudml.org/doc/247378},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Sekigawa, Kouei
AU - Suga, Hiroshi
AU - Vanhecke, Lieven
TI - Four-dimensional curvature homogeneous spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 2
SP - 261
EP - 268
AB - We prove that a four-dimensional, connected, simply connected and complete Riemannian manifold which is curvature homogeneous up to order two is a homogeneous Riemannian space.
LA - eng
KW - Riemannian manifold; curvature homogeneous spaces; homogeneous spaces; locally homogeneous space; Singer's estimate
UR - http://eudml.org/doc/247378
ER -

References

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  1. Bérard Bergery L., Les espaces homogènes riemanniens de dimension 4 , Géométrie riemannienne en dimension 4, Séminaire A. Besse, Cedic, Paris, 1981, 40-60. MR0769130
  2. Derdziński A., preprint, . 
  3. Gromov M., Partial differential equations, Ergeb. Math. Grenzgeb. 3 Folge 9, Springer-Verlag, Berlin, Heidelberg, New York, 1987. 
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  5. Kowalski O., A note to a theorem by K. Sekigawa, Comment. Math. Univ. Carolinae 30 (1989), 85-88. (1989) Zbl0679.53043MR0995705
  6. Kowalski O., Tricerri F., Vanhecke L., Exemples nouveaux de variétés riemanniennes non- homogènes dont le tenseur de courbure est celui d'un espace symétrique riemannien, C.R. Acad. Sci. Paris Sér. I 311 (1990), 355-360. (1990) MR1071643
  7. Kowalski O., Tricerri F., Vanhecke L., Curvature homogeneous Riemannian manifolds, J. Math. Pures Appl., to appear. Zbl0836.53029MR1193605
  8. Kowalski O., Tricerri F., Vanhecke L., Curvature homogeneous spaces with a solvable Lie group as homogeneous model, to appear. Zbl0762.53031MR1167378
  9. Sekigawa K., On the Riemannian manifolds of the form B × f F , Kōdai Math. Sem. Rep. 26 (1975), 343-347. (1975) Zbl0304.53019MR0438253
  10. Sekigawa K., On some 3 -dimensional curvature homogeneous spaces, Tensor N.S. 31 (1977), 87-97. (1977) Zbl0356.53016MR0464115
  11. Singer M.I., Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685-697. (1960) Zbl0171.42503MR0131248
  12. Takagi H., On curvature homogeneity of Riemannian manifolds, Tôhoku Math. J. 26 (1974), 581-585. (1974) Zbl0302.53022MR0365417
  13. Tricerri F., Vanhecke L., Curvature homogeneous Riemannian manifolds, Ann. Sci. Ecole Norm. Sup. 22 (1989), 535-554. (1989) Zbl0698.53033MR1026749

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