Akademik Veri Yönetim Sistemi
International Symposium on Differential Geometry and Its Applications, Tunceli, Türkiye, 3 - 04 Temmuz 2025, ss.96-97, (Özet Bildiri)
In this talk, we introduce Lagrangian submersions whose total manifolds are glob- ally conformal Kähler manifolds. We first give the necessary and sufficient condi- tions for the horizontal and vertical distributions of such a submersion to be totally geodesic. Then we examine the harmonicity of these submersions. We show that the Lee vector field of the total manifold of such a submersion cannot be vertical.
When the Lee vector field is horizontal, we prove that the horizontal distribution is integrable and totally geodesic while the fibers are not totally geodesic. After then, we obtain fundamental equations for a curve on the total manifold of such submer- sions to be geodesic. We can therefore give a necessary and sufficient condition for a Lagrangian submersion to be Clairaut. Finally, we prove that if a Lagrangian submersion from a globally 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.