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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
