(untitled) (Journal of Mathematical Study, 2021)
We introduce the concept h-almost Yamabe soliton which extends naturally the almost Yamabe soliton by Barbosa-Ribeiro and obtain some rigidity results concerning h-almost Yamabe solitons. Some condition for a compact h-almost Yamabe soliton to be a gradient soliton is also obtained. Finally, we give some characterizations for a special class of gradient h-almost Yamabe solitons.