Abstract
In the present paper, we consider the non-reductive four-dimensional homogeneous spaces and we classify homogeneous generalized Ricci solitons on these spaces. We show that any non-reductive four-dimensional homogeneous space admits the least in a generalized Ricci soliton. Also, we will prove that non-reductive four-dimensional homogeneous spaces have non-trivial Killing vector fields and these spaces exclusive of types A1, A4 and B2 are Einstein manifold and admit in non-trivial homogeneous Ricci solitons.
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