Statistical conformal killing vector field (SCKVF) on Newtonian gauge space-times

In this paper, we investigate the conformal Killing vector fields in Newtonian gauge space-time and analyze their properties in detail. We focus particularly on the structure of the associated conformal factors and examine several nontrivial special cases. By utilizing the symmetries of affine geometry, we construct an affine connection on the Newtonian gauge space-time without imposing common geometric constraints such as flatness, metric compatibility, or torsion-freeness. From this general connection, we derive a statistical connection, thereby establishing a statistical structure on the Newtonian gauge. Within this framework, we analyze the conformal symmetry of the tensor field K, defined as the difference between the statistical connection and the Levi–Cività connection. Moreover, we characterize the conditions under which a conformal Killing vector field on the underlying manifold also serves as a statistical conformal Killing vector field in the induced statistical geometry.