Tohoku Mathematical Journal

Conformally flat homogeneous pseudo-Riemannian four-manifolds

Giovanni Calvaruso and Amirhesam Zaeim

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We obtain a complete classification of four-dimensional conformally flat homogeneous pseudo-Riemannian manifolds.

Article information

Source
Tohoku Math. J. (2), Volume 66, Number 1 (2014), 31-54.

Dates
First available in Project Euclid: 7 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1396875661

Digital Object Identifier
doi:10.2748/tmj/1396875661

Mathematical Reviews number (MathSciNet)
MR3189478

Zentralblatt MATH identifier
1296.53136

Subjects
Primary: 53C50: Lorentz manifolds, manifolds with indefinite metrics
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords
Conformally flat manifolds homogeneous pseudo-Riemannian manifolds Ricci operator Segre types

Citation

Calvaruso, Giovanni; Zaeim, Amirhesam. Conformally flat homogeneous pseudo-Riemannian four-manifolds. Tohoku Math. J. (2) 66 (2014), no. 1, 31--54. doi:10.2748/tmj/1396875661. https://projecteuclid.org/euclid.tmj/1396875661


Export citation

References

  • A. Bowers, Classification of three-dimensional real Lie algebras, available online at the webpage math.ucsd.edu/ abowers/downloads/survey/3d_Lie_alg_classify.pdf
  • M. Brozos-Vazquez, E. Garcia-Rio, P. Gilkey, S. Nikcevic and R. Vazquez-Lorenzo, The geometry of Walker manifolds, Synth. Lect. Math. Stat 5, Morgan & Claypool Publishers, Williston, VT, 2009.
  • G. Calvaruso, Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds, Geom. Dedicata 127 (2007), 99–119.
  • G. Calvaruso and A. Zaeim, Four-dimensional homogeneous Lorentzian manifolds, Monaths. Math., to appear. DOI: 10.1007/s00605-013-588-9.
  • M. Chaichi, E. Garcia-Rio and Y. Matsushita, Curvature properties of four-dimensional Walker metrics, Classical Quantum Gravity 22 (2005), 559–577.
  • M. Chaichi and A. Zaeim, Locally homogeneous four-dimensional manifolds of signature (2,2), Math. Phys. Anal. Geom. 16 (2013), 345–361.
  • K. Honda, Conformally flat semi-Riemannian manifolds with commuting curvature and Ricci operators, Tokyo J. Math. 26 (2003), 241–260.
  • K. Honda and K. Tsukada, Three-dimensional conformally flat homogeneous Lorentzian manifolds, J. Phys. A 40 (2007), 831–851.
  • K. Honda and K. Tsukada, Conformally flat homogeneous Lorentzian manifolds, Proceedings of the conference “GELOGRA”, Granada (Spain) 2011, to appear.
  • B. Komrakov Jnr., Einstein-Maxwell equation on four-dimensional homogeneous spaces, Lobachevskii J. Math. 8 (2001), 33–165.
  • P. R. Law, Algebraic classification of the Ricci curvature tensor and spinor for neutral signature in four dimensions, arXiv:1008.0444v1, 2010.
  • S. Rahmani, Métriques de Lorentz sur les groupes de Lie unimodulaires de dimension trois, J. Geom. Phys. 9 (1992), 295–302.
  • P. Ryan, A note on conformally flat spaces with constant scalar curvature, Proceedings of the Thirteenth Biennial Seminar of the Canadian Mathematical Congress, Vol. 2 (On Differential Topology, Differential Geometry and Applications, Dalhousie Univ., Halifax, N.S., 1971), pp. 115–124, Canad. Math. Congr., Montreal, Que., 1972.
  • I. M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685–697.
  • H. Stephani, D. Kramer, M. Maccallum, C. Hoenselaers and E. Herlt, Exact solutions of Einstein's field equations, Cambridge Monographs on Mathematical Physics, 2nd. rev. Ed., Cambridge University Press, 2009.
  • S. Sternberg, Lectures on differential geometry, Prentice-Hall, Englewood Cliffs, N.J., 1964.
  • H. Takagi, Conformally flat Riemannian manifolds admitting a transitive group of isometries, I,II, Tohôku Math. J. 27 (1975), 103–110 and 445–451.