Geometric Characterizations of {\delta}-Almost Yam- abe Solitons with QSNM Connections

TL;DR

This paper explores the geometric properties of { extdelta}-almost Yamabe solitons on paracontact metric manifolds with a quarter-symmetric non-metric connection, providing classification results and conditions for different types of solitons.

Contribution

It offers new classification results and conditions for { extdelta}-almost Yamabe solitons on paracontact manifolds with a specific connection, including examples.

Findings

Classification under collinearity with Reeb vector fields

Conditions for expanding, steady, or shrinking solitons

Explicit example illustrating theoretical results

Abstract

In this paper, we investigate the geometric structure of {\delta}- 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 {\lambda} and the structure functions of the manifold. Finally, we present an example that illustrates our results.