# Article

Full entry | PDF   (0.1 MB)
Keywords:
Riemannian manifold; curvature homogeneous space
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.
References:
[BKV] Boeckx E., Kowalski O., Vanhecke L.: Nonhomogeneous relatives of symmetric spaces. to appear in Differential Geometry and its Applications. MR 1264908
[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
[KN] Kobayashi S., Nomizu K.: Foundations of Differential Geometry I. Interscience Publishers, New York, 1983. Zbl 0119.37502
[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. MR 1071643 | Zbl 0713.53028
[KTV2] Kowalski O., Tricerri F., Vanhecke L.: Curvature homogeneous Riemannian manifolds. J. Math. Pures Appl. 71 (1992), 471-501. MR 1193605 | Zbl 0836.53029
[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. MR 1167378 | Zbl 0762.53031
[Mi] Milnor J.: Curvatures of left invariant Lie groups. Adv. in Math. 21 (1976), 293-329. MR 0425012
[Se1] Sekigawa K.: On some 3-dimensional Riemannian manifolds. Hokkaido Math. J. 2 (1973), 259-270. MR 0353204 | Zbl 0266.53034
[Se2] Sekigawa K.: On some 3-dimensional curvature homogeneous spaces. Tensor, N.S. 31 (1977), 87-97. MR 0464115 | Zbl 0356.53016
[Si] Singer I.M.: Infinitesimally homogeneous spaces. Comm. Pure Appl. Math. 13 (1960), 685-697. MR 0131248 | Zbl 0171.42503
[T] Tsukada T.: Curvature homogeneous hypersurfaces immersed in a real space form. Tôhoku Math. J. 40 (1988), 221-244. MR 0943821 | Zbl 0651.53037
[Ya] Yamato K.: A characterization of locally homogeneous Riemannian manifolds of dimension 3. Nagoya Math. J. 123 (1991), 77-90. MR 1126183

Partner of