Some results on RicciBourguignon and RicciBourguignon almost solitons
Shubham Dwivedi,
2018.09.28
http://arxiv.org/abs/1809.11103
We prove some results for the solitons of the RicciBourguignon flow,
generalizing corresponding results for Ricci solitons. Taking motivation from
Ricci almost solitons, we then introduce the notion of RicciBourguignon
$almost$ solitons and prove some results about them which generalize previous
results for Ricci almost solitons. We also derive integral formulas for compact
gradient RicciBourguignon solitons and compact gradient RicciBourguignon
almost solitons. Finally, using the integral formula we show that a compact
gradient RicciBourguignon almost soliton is isometric to an Euclidean sphere
if it has constant scalar curvature or its associated vector field is
conformal.
