Geometric Characterizations of δ-Almost Yam- abe Solitons with QSNM Connections

Abstract

In this paper, we investigate the geometric structure of δ- almost Yamabe solitons on paracontact metric manifolds endowed with a quarter-symmetric non-metric connection {\nabla}. We establish a series of classification results under specific assumptions, including collinearity with the Reeb vector fields, infinitesimal contact transformations, torse- forming, conformal and {X}-Ric vector fields on the potential vector field. Furthermore, we derive conditions under which the soliton is expand- ing, steady, or shrinking based on the relationship among the scalar curvature {r}, the soliton function λ and the structure functions of the manifold. Finally, we present an example that illustrates our results.

The paper is being withdrawn due to the discovery of significant errors in the results, which require substantial revision before resubmission