Abstract
We consider gradient Ricci solitons, conformal to an n-dimensional pseudo-Euclidean space, which are invariant under the action of an (n − 1)-dimensional translation group. We provide all such solutions in the case of steady gradient Ricci solitons.
Similar content being viewed by others
References
W. Batat, M. Brozos-Vásquez, E. García-Río and S. Gavino-Fernández, Ricci solitons on Lorentzian manifolds with large isometry groups, Bulletin of the London Mathematical Society 43 (2011), 1219–1227.
A. L. Besse, Einstein Manifolds, Springer-Verlag, Berlin, 1987.
M. Brozos-Vásquez, G. Calvaruso, E. García-Río and S. Gavino-Fernández, Threedimensional Lorentzian homogeneous Ricci solitons, Israel Journal of Mathematics 188 (2012), 385–403.
M. Brozos-Vásquez, E. García-Río and S. Gavino-Fernández, Locally conformally flat Lorentzian gradient Ricci solitons, Journal of Geometric Analysis 13 (2013), 1196–1212.
R. Bryant, Local existence of gradient Ricci solitons, unpublished.
H. D. Cao and Q. Chen, On locally conformally flat steady gradient solitons, Transactions of the American Mathematical Society 364 (2012), 2377–2391.
H. T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York, 1962.
M. Fernández-López and E. García-Río, Rigidity of shrinking Ricci solitons, Mathematische Zeitschrift 269 (2011), 461–466.
K. Onda, Lorentz Ricci solitons on 3-dimensional Lie groups, Geometriae Dedicata 147 (2010), 313–322.
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by CNPq.
Partially supported by CAPES-PROCAD.
Partially supported by CNPq and CAPES-PROCAD.
Rights and permissions
About this article
Cite this article
Barbosa, E., Pina, R. & Tenenblat, K. On gradient Ricci solitons conformal to a pseudo-Euclidean space. Isr. J. Math. 200, 213–224 (2014). https://doi.org/10.1007/s11856-014-0014-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11856-014-0014-6