Remarks on scalar curvature of gradient Ricci-Bourguignon sollitons

Abstract

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.