| Title:
|
Four-dimensional curvature homogeneous spaces (English) |
| Author:
|
Sekigawa, Kouei |
| Author:
|
Suga, Hiroshi |
| Author:
|
Vanhecke, Lieven |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
261-268 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Riemannian manifold |
| Keyword:
|
curvature homogeneous spaces |
| Keyword:
|
homogeneous spaces |
| MSC:
|
53C20 |
| MSC:
|
53C30 |
| idZBL:
|
Zbl 0763.53043 |
| idMR:
|
MR1189656 |
| . |
| Date available:
|
2009-01-08T17:55:26Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118493 |
| . |
| Reference:
|
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| Reference:
|
[2] Derdziński A.: preprint.. |
| Reference:
|
[3] Gromov M.: Partial differential equations.Ergeb. Math. Grenzgeb. 3 Folge 9, Springer-Verlag, Berlin, Heidelberg, New York, 1987. |
| Reference:
|
[4] Jensen G.: Homogeneous Einstein spaces in dimension four.J. Differential Geom. 3 (1969), 309-349. MR 0261487 |
| Reference:
|
[5] Kowalski O.: A note to a theorem by K. Sekigawa.Comment. Math. Univ. Carolinae 30 (1989), 85-88. Zbl 0679.53043, MR 0995705 |
| Reference:
|
[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. MR 1071643 |
| Reference:
|
[7] Kowalski O., Tricerri F., Vanhecke L.: Curvature homogeneous Riemannian manifolds.J. Math. Pures Appl., to appear. Zbl 0836.53029, MR 1193605 |
| Reference:
|
[8] Kowalski O., Tricerri F., Vanhecke L.: Curvature homogeneous spaces with a solvable Lie group as homogeneous model.to appear. Zbl 0762.53031, MR 1167378 |
| Reference:
|
[9] Sekigawa K.: On the Riemannian manifolds of the form $B\times _f F$.Kōdai Math. Sem. Rep. 26 (1975), 343-347. Zbl 0304.53019, MR 0438253 |
| Reference:
|
[10] Sekigawa K.: On some $3$-dimensional curvature homogeneous spaces.Tensor N.S. 31 (1977), 87-97. Zbl 0356.53016, MR 0464115 |
| Reference:
|
[11] Singer M.I.: Infinitesimally homogeneous spaces.Comm. Pure Appl. Math. 13 (1960), 685-697. Zbl 0171.42503, MR 0131248 |
| Reference:
|
[12] Takagi H.: On curvature homogeneity of Riemannian manifolds.Tôhoku Math. J. 26 (1974), 581-585. Zbl 0302.53022, MR 0365417 |
| Reference:
|
[13] Tricerri F., Vanhecke L.: Curvature homogeneous Riemannian manifolds.Ann. Sci. Ecole Norm. Sup. 22 (1989), 535-554. Zbl 0698.53033, MR 1026749 |
| . |
