| Title:
|
Nonhomogeneous Riemannian 3-manifolds with distinct constant Ricci eigenvalues (English) |
| Author:
|
Kowalski, Oldřich |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
3 |
| Year:
|
1993 |
| Pages:
|
451-457 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We extend a construction by K. Yamato [Ya] to obtain new explicit examples of Riemannian 3-manifolds as in the title. Some of these examples have an interesting geometrical interpretation. (English) |
| Keyword:
|
Riemannian manifold |
| Keyword:
|
curvature homogeneous space |
| MSC:
|
53C20 |
| MSC:
|
53C21 |
| MSC:
|
53C25 |
| MSC:
|
53C30 |
| MSC:
|
53C40 |
| idZBL:
|
Zbl 0789.53024 |
| idMR:
|
MR1243077 |
| . |
| Date available:
|
2009-01-08T18:05:15Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118602 |
| . |
| Reference:
|
[BKV] Boeckx E., Kowalski O., Vanhecke L.: Nonhomogeneous relatives of symmetric spaces.to appear in Differential Geometry and its Applications. MR 1264908 |
| Reference:
|
[K] Kowalski O.: A classification of Riemannian 3-manifolds with constant principal Ricci curvatures $\varrho _1=\varrho _2\neq \varrho _3$.to appear in Nagoya Math. J. MR 1253692 |
| Reference:
|
[KN] Kobayashi S., Nomizu K.: Foundations of Differential Geometry I.Interscience Publishers, New York, 1983. Zbl 0119.37502 |
| Reference:
|
[KTV1] Kowalski O., Tricerri F., Vanhecke L.: New examples of non-homogeneous Riemannian manifolds whose curvature tensor is that of a Riemannian symmetric space.C.R. Acad. Sci. Paris, Sér. I, 311 (1990), 355-360. Zbl 0713.53028, MR 1071643 |
| Reference:
|
[KTV2] Kowalski O., Tricerri F., Vanhecke L.: Curvature homogeneous Riemannian manifolds.J. Math. Pures Appl. 71 (1992), 471-501. Zbl 0836.53029, MR 1193605 |
| Reference:
|
[KTV3] Kowalski O., Tricerri F., Vanhecke L.: Curvature homogeneous spaces with a solvable Lie group as homogeneous model.J. Math. Soc. Japan 44 (1992), 461-484. Zbl 0762.53031, MR 1167378 |
| Reference:
|
[Mi] Milnor J.: Curvatures of left invariant Lie groups.Adv. in Math. 21 (1976), 293-329. MR 0425012 |
| Reference:
|
[Se1] Sekigawa K.: On some 3-dimensional Riemannian manifolds.Hokkaido Math. J. 2 (1973), 259-270. Zbl 0266.53034, MR 0353204 |
| Reference:
|
[Se2] Sekigawa K.: On some 3-dimensional curvature homogeneous spaces.Tensor, N.S. 31 (1977), 87-97. Zbl 0356.53016, MR 0464115 |
| Reference:
|
[Si] Singer I.M.: Infinitesimally homogeneous spaces.Comm. Pure Appl. Math. 13 (1960), 685-697. Zbl 0171.42503, MR 0131248 |
| Reference:
|
[T] Tsukada T.: Curvature homogeneous hypersurfaces immersed in a real space form.Tôhoku Math. J. 40 (1988), 221-244. Zbl 0651.53037, MR 0943821 |
| Reference:
|
[Ya] Yamato K.: A characterization of locally homogeneous Riemannian manifolds of dimension 3.Nagoya Math. J. 123 (1991), 77-90. MR 1126183 |
| . |
