Para-Sasakian Manifold Admitting Ricci-Yamabe Solitons With Quarter Symmetric Metric Connection

In the year 2019, Guler and Crasmareanu [6] conducted an investigation into another geometric flow known as the Ricci-Yamabe map. This map is nothing but a scalar combination of the Ricci and the Yamabe flow [7]. The primary objective of the current paper is to provide a characterization of a Ricci Yamabe soliton on a para-Sasakian manifold [17]. To commence, we prove that a para-Sasakian manifold admits a nearly quasi-Einstein manifold. Moreover, we discuss whether such a manifold is shrinking, expanding, or steady. Subsequently, we generalize these findings to Ricci-Yamabe solitons on para-Sasakian manifolds equipped with a quarter symmetric metric connection. Lastly, we furnish an illustration of a three-dimensional para-Sasakian manifold admitting a Ricci-Yamabe soliton which satisfies our results.