Some important characterizations of pseudo W8-curvature tensor within the framework of (LCS)n-manifolds

Abstract

This study investigates the pseudo W₈-curvature tensor bW₈ on (LCS)_n-manifolds. The study examines pseudoW8-flat and ζ-pseudo W₈-flat (LCS)_n-manifolds, leading to notable findings. An (LCS)_n-manifold satisfying the φ- pseudo W₈- semisymmetric condition is found to be a generalized η-Einstein manifold. Curvature conditions bW₈ ・Q = 0, bW₈ ・R = 0, and R(ζ,H₁)・bW₈ = 0 lead to the manifold being Einstein or η-Einstein. The pseudo W8-Ricci pseudosymmetric condition and η-Ricci solitons under bW₈(ζ,H₁) ・S = 0 and S(ζ,H₁) ・ bW₈ = 0 yield notable results. Conservative, irrotational, cyclic parallel, and η-parallel Ricci tensors are also analyzed.