Quasi Invariant Hypersurfaces of LP-Sasakian Manifolds

This study explores the geometric characterization of hypersurfaces in 3-dimensional Lorentzian para-Sasakian (LP-Sasakian) manifolds. We establish that an immersed hypersurface of a 3-dimensional LP-Sasakian manifold  is invariant if and only if the structure induced on by the ambient LP-Sasakian structure - namely,  - constitutes a 3-dimensional LP-Sasakian structure. This equivalence provides a necessary and sufficient condition for identifying invariant hypersurfaces purely in terms of their intrinsic geometry, bridging the behavior of the ambient manifold with that of its hypersurfaces.