Three-dimensional Lorentzian homogeneous Ricci solitons

Ricci solitons on Lorentzian Walker three-manifolds

“…It is clear that equation (4.3) is a special case of (4.2). Thus, Theorem 4.1 yields at once the following Corollary 4.3 [2]. Any three-dimensional symmetric strictly Walker metric is a Ricci soliton.…”

“…Homogeneous Ricci solitons in three-dimensional Lorentzian spaces were classified in [2], showing that, with respect to the Riemannian case, Lorentzian settings allow many non-trivial solutions to the Ricci solitons equation. These results make it interesting to further investigate Ricci solitons on Lorentzian three-manifolds.…”

Three-Dimensional Homogeneous Generalized Ricci Solitons

“…In this way, (1.1) will be transformed into a system of algebraic equations, which we can solve, obtaining a complete classification of three-dimensional left-invariant generalized Ricci solitons, and determining several new solutions of (1.1). We recall that the study of three-dimensional Ricci solitons already showed some interesting differences arising between the Riemannian case (for which left-invariant solutions do not occur [8]) and the Lorentzian one, where several left-invariant solutions exist [1]. Also for the broader class of generalized Ricci solitons, interesting differences show up between the Riemannian and the Lorentzian cases.…”

Ricci solitons on low-dimensional generalized symmetric spaces

“…With respect to the notations introduced in [15], in equation (2.1) we used µ instead of λ, which we reserved for the Ricci soliton equation (1.1). Depending on the values of ε and µ, these metrics can attain any possible signature: (3, 0), (0, 3), (2, 1), (1,2).…”