# On special Riemannian $3$-manifolds with distinct constant Ricci eigenvalues

Oldřich Kowalski; Zdeněk Vlášek

Mathematica Bohemica (1999)

- Volume: 124, Issue: 1, page 45-66
- ISSN: 0862-7959

## Access Full Article

top## Abstract

top## How to cite

topKowalski, Oldřich, and Vlášek, Zdeněk. "On special Riemannian $3$-manifolds with distinct constant Ricci eigenvalues." Mathematica Bohemica 124.1 (1999): 45-66. <http://eudml.org/doc/248457>.

@article{Kowalski1999,

abstract = {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.},

author = {Kowalski, Oldřich, Vlášek, Zdeněk},

journal = {Mathematica Bohemica},

keywords = {Riemannian manifold; constant principal Ricci curvatures; Riemannian manifold; constant principal Ricci curvatures},

language = {eng},

number = {1},

pages = {45-66},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On special Riemannian $3$-manifolds with distinct constant Ricci eigenvalues},

url = {http://eudml.org/doc/248457},

volume = {124},

year = {1999},

}

TY - JOUR

AU - Kowalski, Oldřich

AU - Vlášek, Zdeněk

TI - On special Riemannian $3$-manifolds with distinct constant Ricci eigenvalues

JO - Mathematica Bohemica

PY - 1999

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 124

IS - 1

SP - 45

EP - 66

AB - 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.

LA - eng

KW - Riemannian manifold; constant principal Ricci curvatures; Riemannian manifold; constant principal Ricci curvatures

UR - http://eudml.org/doc/248457

ER -

## References

top- E. Boeckx O. Kowalski. L. Vanhecke, Riemannian Manifolds of Conullity Two, World Scientific Publishers. 1990 MR1462887
- P. Bueken, 10.1063/1.531626, J. Math Phys. 37 (1990), 4062-4075. (1990) MR1400834DOI10.1063/1.531626
- O. Kowalski, A classification of Riemannian 3-manifolds with constant principal Ricci curvatures ${\rho}_{1}={\rho}_{2}\ne {\rho}_{3}$, Nagoya Math. J. 132 (1993), 1-36. (1993) MR1253692
- O. Kowalski, Nonhomogeneous Riemannian 3-manifolds with distinct constant Ricci eigenvalues, Comment. Math. Univ. Carotin. 34 (1993), 451-457. (1993) Zbl0789.53024MR1243077
- O. Kowalski F. Prüfer, 10.1007/BF01450473, Math. Ann. 300 (1994), 17-28. (1994) MR1289828DOI10.1007/BF01450473
- O. Kowalski F. Prüfer, 10.4171/ZAA/662, Z. Anal. Anwendungen 14 (1995), 43-58. (1995) MR1327491DOI10.4171/ZAA/662
- O. Kowalski M. Sekizawa, Local isometry classes of Riemannian 3-manifolds with constant Ricci eigenvalues ${\rho}_{1}={\rho}_{2}\ne {\rho}_{3}>0$, Arch. Math. (Brno) 32 (1996), 137-145. (1996) MR1407345
- 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. (1998) MR1610731
- I. M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1990), 685-697. (1990) MR0131248
- A. Spiro F. Tricerri, 3-diinensioual Riemannian metrics with prescribed Ricci principal curvatures, J. Math. Pures. Appl. 74 (1995), 253-271. (1995) MR1327884
- K. Yamato, A characterization of locally homogeneous Riemannian manifolds of dimension 3, Nagoya Math. J. 123 (1991), 77-90. (1991) MR1126183

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.