η-Ricci-Yamabe Solitons in the Framework of LP-Kenmotsu Manifolds

Abstract

This paper examines the geometric characteristics of η-Ricci-Yamabe solitons within the framework of LP-Kenmotsu manifolds. A key focus is on determining conditions under which these solitons satisfy the curvature relation R . S = 0. Additionally, we explore their behavior in quasi-conformally flat settings. Further, we establish results for solitons on manifolds exhibiting quasi-conformal Ricci semi-symmetry, φ-quasi-conformal semi-symmetry, and φ-Ricci symmetry, alongside conditions involving the Codazzi-type Ricci tensor and the cyclic parallel Ricci tensor. To substantiate our findings, we construct an explicit example demonstrating the existence of such solitons in LP-Kenmotsu manifolds