About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

First Page Preview
Kowalski, Oldřich ; Vlášek, Zdeněk
On special Riemannian $3$-manifolds with distinct constant Ricci eigenvalues. (English). Mathematica Bohemica, vol. 124 (1999), issue 1, pp. 45-66
MSC: 53B20, 53C20, 53C21, 53C25, 53C30 | MR 1687417 | Zbl 0934.53027 | DOI: 10.21136/MB.1999.125981
Keywords:
Riemannian manifold; constant principal Ricci curvatures
Summary:
The first author and F. Prufer gave an explicit classification of all Riemannian 3-manifolds with distinct constant Ricci eigenvalues and satisfying additional geometrical conditions. The aim of the present paper is to get the same classification under weaker geometrical conditions.
References:
[1] E. Boeckx O. Kowalski. L. Vanhecke: Riemannian Manifolds of Conullity Two. World Scientific Publishers. 1990 MR 1462887
[2] P. Bueken: Three-dimensional Riemannian manifolds with constant principal Ricci curvatures $\rho_1 = \rho_2 \neq \rho_3$. J. Math Phys. 37 (1990), 4062-4075. DOI 10.1063/1.531626 | MR 1400834
[3] O. Kowalski: A classification of Riemannian 3-manifolds with constant principal Ricci curvatures $\rho_1 = \rho_2 \neq \rho_3$. Nagoya Math. J. 132 (1993), 1-36. MR 1253692
[4] O. Kowalski: Nonhomogeneous Riemannian 3-manifolds with distinct constant Ricci eigenvalues. Comment. Math. Univ. Carotin. 34 (1993), 451-457. MR 1243077 | Zbl 0789.53024
[5] O. Kowalski F. Prüfer: On Riemannian 3-manifolds with distinct constant Ricci eigenvalues. Math. Ann. 300 (1994), 17-28. DOI 10.1007/BF01450473 | MR 1289828
[6] O. Kowalski F. Prüfer: A classification of special Riemannian 3-manifolds with distinct constant Ricci eigenvalues. Z. Anal. Anwendungen 14 (1995), 43-58. DOI 10.4171/ZAA/662 | MR 1327491
[7] O. Kowalski M. Sekizawa: Local isometry classes of Riemannian 3-manifolds with constant Ricci eigenvalues $\rho_1 = \rho_2 \neq \rho_3 > 0$. Arch. Math. (Brno) 32 (1996), 137-145. MR 1407345
[8] O. Kowalski Z. Vlášek: Classification of Riemannian 3-manifolds with distinct constant principal Ricci curvatures. Bull. Belg, Math. Soc. Simon Stevin 5 (1998), 59-68. DOI 10.36045/bbms/1103408965 | MR 1610731
[9] I. M. Singer: Infinitesimally homogeneous spaces. Comm. Pure Appl. Math. 13 (1990), 685-697. MR 0131248
[10] A. Spiro F. Tricerri: 3-diinensioual Riemannian metrics with prescribed Ricci principal curvatures. J. Math. Pures. Appl. 74 (1995), 253-271. MR 1327884
[11] K. Yamato: A characterization of locally homogeneous Riemannian manifolds of dimension 3. Nagoya Math. J. 123 (1991), 77-90. DOI 10.1017/S0027763000003652 | MR 1126183
Partner of
EuDML logo