| Title:
|
On special Riemannian $3$-manifolds with distinct constant Ricci eigenvalues (English) |
| Author:
|
Kowalski, Oldřich |
| Author:
|
Vlášek, Zdeněk |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
45-66 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Riemannian manifold |
| Keyword:
|
constant principal Ricci curvatures |
| MSC:
|
53B20 |
| MSC:
|
53C20 |
| MSC:
|
53C21 |
| MSC:
|
53C25 |
| MSC:
|
53C30 |
| idZBL:
|
Zbl 0934.53027 |
| idMR:
|
MR1687417 |
| DOI:
|
10.21136/MB.1999.125981 |
| . |
| Date available:
|
2009-09-24T21:34:59Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125981 |
| . |
| Reference:
|
[1] E. Boeckx O. Kowalski. L. Vanhecke: Riemannian Manifolds of Conullity Two.World Scientific Publishers. 1990 MR 1462887 |
| Reference:
|
[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. MR 1400834, 10.1063/1.531626 |
| Reference:
|
[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 |
| Reference:
|
[4] O. Kowalski: Nonhomogeneous Riemannian 3-manifolds with distinct constant Ricci eigenvalues.Comment. Math. Univ. Carotin. 34 (1993), 451-457. Zbl 0789.53024, MR 1243077 |
| Reference:
|
[5] O. Kowalski F. Prüfer: On Riemannian 3-manifolds with distinct constant Ricci eigenvalues.Math. Ann. 300 (1994), 17-28. MR 1289828, 10.1007/BF01450473 |
| Reference:
|
[6] O. Kowalski F. Prüfer: A classification of special Riemannian 3-manifolds with distinct constant Ricci eigenvalues.Z. Anal. Anwendungen 14 (1995), 43-58. MR 1327491, 10.4171/ZAA/662 |
| Reference:
|
[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 |
| Reference:
|
[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. MR 1610731, 10.36045/bbms/1103408965 |
| Reference:
|
[9] I. M. Singer: Infinitesimally homogeneous spaces.Comm. Pure Appl. Math. 13 (1990), 685-697. MR 0131248 |
| Reference:
|
[10] A. Spiro F. Tricerri: 3-diinensioual Riemannian metrics with prescribed Ricci principal curvatures.J. Math. Pures. Appl. 74 (1995), 253-271. MR 1327884 |
| Reference:
|
[11] K. Yamato: A characterization of locally homogeneous Riemannian manifolds of dimension 3.Nagoya Math. J. 123 (1991), 77-90. MR 1126183, 10.1017/S0027763000003652 |
| . |
