This manuscript investigates conformal η-Ricci–Yamabe solitons of type (κ,l) on Kählerian Norden space-time admitting a Kählerian Norden torse-forming vector field. Necessary conditions are obtained under which the soliton exhibits expanding, steady, or shrinking behavior. The analysis is further extended to several physically relevant fluid models, including dark fluid, dust fluid, stiff matter, and radiational fluid, and the corresponding geometric constraints are derived. In addition, structural results are established for Kählerian Norden space-times with a vanishing space–matter tensor and with a divergence-free matter tensor, highlighting their influence on the curvature geometry. The study also addresses several intrinsic curvature conditions of the space-time, such as conformal flatness, Ricci semi-symmetry, Ricci recurrence, and pseudo-Ricci symmetry, leading to a collection of geometric and physical characterizations. The results obtained provide a unified geometric framework linking Ricci–Yamabe soliton structures, fluid dynamics, and curvature properties within the setting of Kählerian Norden geometry.
Nazra et al. (Sat,) studied this question.