In this paper, we work on the scalar curvature of complete non-compact gradient Ricci-Bourguignon solitons and prove several results. In the first part, we prove that, with some conditions, any complete non-compact gradient Ricci-Bourguignon soliton has nonnegative scalar curvature. In the second part, we show that the quadratic decay at infinity of the Ricci curvature of complete non-compact gradient Ricci-Bourguignon soliton has constant scalar curvature.

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关于梯度 Ricci-Bourguignon 孤子的标量曲率的备注

在本文中，我们研究了完全非紧致梯度 Ricci-Bourguignon 孤子的标量曲率并证明了几个结果。在第一部分中，我们证明，在某些条件下，任何完全非紧梯度 Ricci-Bourguignon 孤子都具有非负标量曲率。在第二部分中，我们展示了完全非紧梯度 Ricci-Bourguignon 孤子的 Ricci 曲率在无穷远处的二次衰减具有恒定的标量曲率。