An introduction to gradient solitons on statistical Poisson manifold and perfect fluid Poisson manifold

Abstract

In this article, we introduce the idea of statistical Poisson manifold and perfect fluid Poisson manifold. Then, we investigate the well known almost solitons like Ricci soliton, Yamabe solitons or Einstein solitons on Poisson manifold and discuss the statistical structures. Next, we find a volume formula of the Poisson manifold and discuss the bounds of |Ric|2 for gradient solitons. Afterward, we study statistical structure on a perfect fluid Poisson manifold. Then, we obtain the volume formula and bounds of |Ric|2 for perfect fluid Poisson manifold.