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

Ali H. Hakami and Mohd. Danish Siddiqi ()
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Ali H. Hakami: Department of Mathematics, College of Science, Jazan University, P.O. Box 277, Jazan 4512, Saudi Arabia
Mohd. Danish Siddiqi: Department of Mathematics, College of Science, Jazan University, P.O. Box 277, Jazan 4512, Saudi Arabia

Mathematics, 2023, vol. 11, issue 15, 1-19

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

Keywords: anti-invariant submersion; Lagrangian submersion; Lorentzian para-Sasakian manifold; homotopy groups (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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