We consider almost Riemann solitons \((V,\lambda )\) in a Riemannian manifold and underline their relation to almost Ricci solitons. When V is of gradient type, using Bochner formula, we explicitly express the function \(\lambda \) by means of the gradient vector field V and illustrate the result with suitable examples. Moreover, we deduce some properties for the particular cases when the potential vector field of the soliton is solenoidal or torse-forming, with a special view towards curvature.

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关于带有梯度或扭转形成矢量场的几乎黎曼孤子的评论

我们考虑黎曼流形中的几乎黎曼孤子\（（V，\ lambda）\）并强调它们与几乎黎氏孤子的关系。当V为梯度类型时，使用Bochner公式，我们通过梯度矢量场V明确表示函数\（\ lambda \），并用合适的示例说明结果。此外，我们针对孤子的势矢量场为螺线管形或扭转形时的特殊情况推导了一些性质，并特别关注曲率。