Generalized Ricci Solitons of Three-Dimensional Lorentzian Lie Groups Associated Canonical Connections and Kobayashi-Nomizu Connections

Abstract

In this paper, we study the affine generalized Ricci solitons on three-dimensional Lorentzian Lie groups associated canonical connections and Kobayashi-Nomizu connections and we classifying these left-invariant affine generalized Ricci solitons with some product structure.

Generalized Ricci Solitons on Non-reductive Four-Dimensional Homogeneous Spaces

“…◻ Remark The cases (3)-( 6) of the Theorem 3.6 imply that a non-reductive fourdimensional homogeneous pseudo-Riemannian manifold (M, g) corresponding to Lie algebra 1 has non-trivial Killing vector fields. The cases (1) and (2) show that the manifold (M, g) is an Einstein manifold. Also, from the cases (3)-( 5) of the Theorem 3.6 we conclude that (M, g) is a non-trivial homogeneous Ricci soliton.…”

“…Calvaruso and Fino [10] studied the Ricci solitons on non-reductive four-dimensional homogeneous spaces. Also, see [2,3,5,19] for some results of Ricci solitons on homogeneous manifolds.…”

ًRicci bi-conformal vector fields on Lorentzian five dimensional two-step nilpotent Lie groups

“…Wears in [16] studied Lorentzian Ricci solitons on simply-connected five-dimensional two-step nilpotent Lie groups which are also connected. For more details, see [1][2][3][4][5][6][13][14][15]. Next, De et al in [9] applying the metric tensor field g and the Ricci tensor field S introduced Ricci bi-conformal vector fields as follows:…”

Affine Generalized Ricci Solitons of Three-Dimensional Lorentzian Lie Groups Associated to Yano Connection

“…He determined their homogenous models and classifying left-invariant generalization Ricci solitons on three-dimensional Lie groups for = 0 . In [2], we classified left-invariant affine generalization Ricci solitons on three-dimensional Lie groups with respect to the canonical connections and the Kobayashi-Nomizu connections with some product structure. Also, in [33] Wang studied affine Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure.…”

“…Motivated by the above works and [2,4,32,36,37], we consider the distribution V = span{e 1 , e 2 } and V ⟂ = span{e 3 } for the three dimensional Lorentzian Lie group G i , i = 1, ⋯ , 7 , with product structure J such that Je 1 = e 1 , Je 2 = e 2 , and Je 3 = −e 3 . Then we classify the affine generalized Ricci solitons associated to the Yano connection.…”