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Remarks on scalar curvature of gradient Ricci-Bourguignon sollitons
Bulletin des Sciences Mathématiques  (IF1.118),  Pub Date : 2021-07-15, DOI: 10.1016/j.bulsci.2021.103034
Rong Mi

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.