We prove that on a K -contact manifold, a Ricci almost soliton is a Ricci soliton if and only if the potential vector field V is a Jacobi field along the Reeb vector field ξ . Then we study contact metric as a Ricci almost soliton with parallel Ricci tensor. To this end, we consider Ricci almost solitons whose potential vector field is a contact vector field and prove some rigidity results.

中文翻译：

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里奇几乎孤子和接触几何

我们证明，在K接触流形上，当且仅当势矢量场V是沿Reeb矢量场ξ的Jacobi场时，Ricci孤子才是Ricci孤子。然后，我们将接触度量作为具有平行Ricci张量的Ricci几乎孤子研究。为此，我们考虑了Ricci几乎是孤子，其潜在矢量场是接触矢量场，并证明了一些刚性结果。