Some Solitons on Anti-Invariant Submanifolds of Para-Sasakian Manifold Admitting Semi-Symmetric Non-Metric Connection

The objective of this study is to investigate ρ-Einstein solitons on submanifolds of a para-Sasakian manifold under certain curvature conditions. The novelty of this work lies in the characterization of ρ-Einstein solitons on anti-invariant submanifolds of a para-Sasakian manifold equipped with a semi-symmetric non-metric connection, where the structure vector field is taken as the potential vector field. We establish several significant results concerning the classification of ρ-Einstein solitons with respect to the W3-curvature tensor and the semi-symmetric non-metric connection. Moreover, we construct a non-trivial example of an anti-invariant submanifold of a five-dimensional para-Sasakian manifold by solving an associated system of partial differential equations.