On the $h$-Almost Yamabe Soliton (Journal of Mathematical Study, 2021)
We introduce the concept $h$-almost Yamabe soliton which extends naturallythe almost Yamabe soliton by Barbosa-Ribeiro and obtain some rigidity results concerning $h$-almost Yamabe solitons. Some condition for a compact $h$-almost Yamabesoliton to be a gradient soliton is also obtained. Finally, we give some characterizations for a special class of gradient $h$-almost Yamabe solitons.
Keywords: Yamabe flow; $h$-almost Yamabe soliton; scalar curvature.