Properties of Anti-Invariant Submersions and Some Applications to Number Theory

In this article, we investigate anti-invariant Riemannian and Lagrangian submersions onto manifolds from the Lorentzian para-Sasakian manifold. We demonstrate that, for these submersions, horizontal distributions are not integrable their fibers totally geodesic. As a result, they geodesic maps. The harmonicity of such is also examined. specifically prove that harmonic when Reeb vector field horizontal. Finally, provide an illustration our findings mention some number-theoretic applications same submersions.