Anti-invariant and Lagrangian submersions from trans-Sasakian manifolds

Abstract

We study anti-invariant and Lagrangian submersions from trans-Sasakian manifolds onto Riemannian manifolds. We prove that the horizontal distributions of such submersions are not integrable and their fibers are not totally geodesic. Consequently, they cannot be totally geodesic maps. We also check that the harmonicity of such submersions. In particular, we show that they cannot be harmonic in the case when the Reeb vector field is horizontal.