Research Information System
Mediterranean Journal of Mathematics, vol.22, no.1, 2025 (SCI-Expanded)
We study Lagrangian submersions whose total manifolds are locally conformal Kähler manifolds. We first investigate the necessary and sufficient conditions for the horizontal and vertical distributions of a Lagrangian submersion from a locally conformal Kähler manifold to be totally geodesic. Then, we examine the harmonicity of these submersions. We prove that the Lee vector field of the total manifold of such a submersion cannot be vertical. In the case of the Lee vector field is horizontal, we show that the horizontal distribution is always integrable and totally geodesic while its fibers cannot be totally geodesic. We obtain fundamental equations for a curve on the total manifold of such submersions to be geodesic. Consequently, we give a necessary and sufficient condition for a Lagrangian submersion to be Clairaut. Finally, we prove that if a Lagrangian submersion from a locally conformal Kähler manifold is a Clairaut submersion, then either its mean curvature vector field is proportional to the horizontal part of its Lee vector field or the vertical distribution of the submersion is one dimensional.