Journal of Mathematical Physics, Analysis, Geometry 2020, vol. 16, No 2, pp. 190-199   https://doi.org/10.15407/mag16.02.190     ( to contents , go back )

### Ricci Solitons of Four-Dimensional Lorentzian Damek-Ricci Spaces

Noura Sidhoumi

École Nationale Polytechnique d'Oran, B.P. 1523 El M'naouar Oran 31000, Algeria
E-mail: sidhoumi noura@yahoo.fr

Received October 8, 2018, revised November 28, 2019.

Abstract

In this paper, we show that the four-dimensional Lorentzian Damek- Ricci spaces are not a Ricci soliton. This is a generalization of the result of Tan and Deng (see [11]) who proved that these spaces are not a Ricci soliton only with respect to the left-invariant vector fields.

Mathematics Subject Classification 2000: 53C5015, 53B30
Key words: Damek-Ricci spaces, Ricci soliton, left-invariant metrics, Lorentzian metrics