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

Abstract

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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.

How to cite

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Kowalski, 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

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

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