From the Ricci flow evolution equation to vanishing theorems for Ricci solitons
arXiv:2005.11392
Abstract
In the paper, we study evolution equations of the scalar and Ricci curvatures under the Hamilton's Ricci flow on a closed manifold and on a complete noncompact manifold. In particular, we study conditions when the Ricci flow is trivial and the Ricci soliton is Ricci flat or Einstein.
10 pages