Akademik Veri Yönetim Sistemi
Journal of Function Spaces, cilt.2025, sa.1, 2025 (SCI-Expanded, Scopus)
This paper investigates four-dimensional almost pure metric plastic manifolds equipped with a specific class of tensor fields known as almost plastic structures. We begin by defining these structures through characteristic algebraic identities and present explicit matrix realizations that capture their essential geometric features. The study then explores the integrability conditions of such structures, revealing how the dependence of a smooth function governs their behavior. Subsequently, we introduce compatible pseudo-Riemannian metrics that satisfy purity conditions relative to the plastic structures, thereby defining almost pure metric plastic pseudo-Riemannian manifolds. A characterization of these manifolds under Levi-Civita parallelism is provided, linking the constancy of structural functions to Kähler-type properties. The final part of the paper is devoted to Walker four-manifolds, a distinguished class of four-dimensional manifolds with metrics admitting parallel null distributions. We construct almost pure metric plastic Walker four-manifolds by specifying an affinor field and adjusting the Walker metric to maintain purity with respect to this structure. The integrability of the plastic structure is thoroughly analyzed, with necessary and sufficient conditions expressed via a smooth structural function. Furthermore, we investigate the existence of Killing vector fields and characterize Ricci soliton structures on these manifolds, establishing precise relations among the structural function, vector fields, and soliton parameters. Overall, the paper provides a detailed study of almost pure metric plastic structures in four dimensions, emphasizing their geometric compatibility, integrability, and soliton dynamics within the Walker four-manifold setting.