On Finslerian Warped Product Gradient Yamabe Solitons

This article aims to study the Finslerian gradient Yamabe solitons on top of warped product manifolds. First, we present some rigidity results related to the warping and potential functions. In the sequel, in order to provide nontrivial examples, we take the warped product base as a double twisted product invariant by the action of a translation and rotation group and, as a result, we characterize the invariant solutions of Finslerian gradient Yamabe solitons. We use this method to provide explicit examples of expanding, shrinking and steady warped product Finslerian gradient Yamabe solitons.