Abstract
Let F=α2β be a Kropina metric on a measure space (M,m) with the navigation data (h,W). In this paper, we give an equivalent characterization for (M,F,m) to be a gradient almost Ricci soliton, which implies that every gradient almost Ricci soliton has vanishing SBH-curvature. Based on this, we prove that (M,F,m) is a gradient almost Ricci soliton if and only if (M,h,f) is a Riemannian gradient almost Ricci soliton, W is a unit Killing vector field on M and f satisfies a differential equation, where f is the potential function f of the measure m (see Theorem 1.2). As an application, we construct some new shrinking, steady and expanding gradient Ricci solitons.
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