On the Ricci operator of locally homogeneous Lorentzian 3-manifolds

Giovanni Calvaruso; Oldrich Kowalski

Open Mathematics (2009)

  • Volume: 7, Issue: 1, page 124-139
  • ISSN: 2391-5455

Abstract

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We determine the admissible forms for the Ricci operator of three-dimensional locally homogeneous Lorentzian manifolds.

How to cite

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Giovanni Calvaruso, and Oldrich Kowalski. "On the Ricci operator of locally homogeneous Lorentzian 3-manifolds." Open Mathematics 7.1 (2009): 124-139. <http://eudml.org/doc/269102>.

@article{GiovanniCalvaruso2009,
abstract = {We determine the admissible forms for the Ricci operator of three-dimensional locally homogeneous Lorentzian manifolds.},
author = {Giovanni Calvaruso, Oldrich Kowalski},
journal = {Open Mathematics},
keywords = {Lorentzian homogeneous spaces; Ricci operator; Segre type; Ricci tensor; symmetric space},
language = {eng},
number = {1},
pages = {124-139},
title = {On the Ricci operator of locally homogeneous Lorentzian 3-manifolds},
url = {http://eudml.org/doc/269102},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Giovanni Calvaruso
AU - Oldrich Kowalski
TI - On the Ricci operator of locally homogeneous Lorentzian 3-manifolds
JO - Open Mathematics
PY - 2009
VL - 7
IS - 1
SP - 124
EP - 139
AB - We determine the admissible forms for the Ricci operator of three-dimensional locally homogeneous Lorentzian manifolds.
LA - eng
KW - Lorentzian homogeneous spaces; Ricci operator; Segre type; Ricci tensor; symmetric space
UR - http://eudml.org/doc/269102
ER -

References

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  2. [2] Bueken P., On curvature homogeneous three-dimensional Lorentzian manifolds, J. Geom. Phys., 1997, 22, 349–362 http://dx.doi.org/10.1016/S0393-0440(96)00037-X[Crossref] Zbl0881.53055
  3. [3] Bueken P., Djoric M., Three-dimensional Lorentz metrics and curvature homogeneity of order one, Ann. Glob. Anal. Geom., 2000, 18, 85–103 http://dx.doi.org/10.1023/A:1006612120550[Crossref] Zbl0947.53037
  4. [4] Calvaruso G., Homogeneous structures on three-dimensional Lorentzian manifolds, J. Geom. Phys., 2007, 57, 1279–1291. Addendum: J. Geom. Phys., 2008, 58, 291–292 http://dx.doi.org/10.1016/j.geomphys.2006.10.005[Crossref] Zbl1112.53051
  5. [5] Calvaruso G., Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds, Geom. Dedicata, 2007, 127, 99–119 http://dx.doi.org/10.1007/s10711-007-9163-7[Crossref] Zbl1126.53044
  6. [6] Calvaruso G., Pseudo-Riemannian 3-manifolds with prescribed distinct constant Ricci eigenvalues, Diff. Geom. Appl., 2008, 26, 419–433 http://dx.doi.org/10.1016/j.difgeo.2007.11.031[Crossref] Zbl1153.53053
  7. [7] Calvaruso G., Three-dimensional homogeneous Lorentzian metrics with prescribed Ricci tensor, preprint Zbl1153.81329
  8. [8] Chaichi M., García-Río E., Vázquez-Abal M.E., Three-dimensional Lorentz manifolds admitting a parallel null vector field, J. Phys. A: Math. Gen., 2005, 38, 841–850 http://dx.doi.org/10.1088/0305-4470/38/4/005[Crossref] Zbl1068.53049
  9. [9] Cordero L.A., Parker P.E., Left-invariant Lorentzian metrics on 3-dimensional Lie groups, Rend. Mat., Serie VII, 1997, 17, 129–155 Zbl0948.53027
  10. [10] Kowalski O., Nonhomogeneous Riemannian 3-manifolds with distinct constant Ricci eigenvalues, Nagoya Math. J., 1993, 132, 1–36 Zbl0789.53024
  11. [11] Kowalski O., Nikčević S.Ž., On Ricci eigenvalues of locally homogeneous Riemannian 3-manifolds, Geom. Dedicata, 1996, 62, 65–72 http://dx.doi.org/10.1007/BF00240002[Crossref] Zbl0859.53034
  12. [12] Kowalski O., Prüfer F., On Riemannian 3-manifolds with distinct constant Ricci eigenvalues, Math. Ann., 1994, 300, 17–28 http://dx.doi.org/10.1007/BF01450473[Crossref] Zbl0813.53020
  13. [13] Milnor J., Curvature of left invariant metrics on Lie groups, Adv. Math., 1976, 21, 293–329 http://dx.doi.org/10.1016/S0001-8708(76)80002-3[Crossref] Zbl0341.53030
  14. [14] O’Neill B., Semi-Riemannian Geometry, Academic Press, New York, 1983 
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