ON ϵ–PARA SASAKIAN MANIFOLDS ADMITTING ∗–CONFORMAL η–RICCI SOLITONS

Abstract

This paper characterizes $\epsilon$--para Sasakian manifolds admitting a $*$--conformal $\eta$--Ricci soliton. We analyze solitons under diverse geometric conditions, namely, generalized Ricci recurrence, flatness of specific $\mathcal{W}_i$--curvature tensors ($i=6,7,8$), and $\phi$--$\mathcal{W}_j$--semisymmetry ($j=3,5$). Cases satisfying $Q \cdot R=0$ and $\phi$--Ricci symmetry are also investigated. The study concludes with an explicit 5-dimensional example proving the soliton's existence.