Riemannian Submersions and Lagrangian Isometric Immerson 1

In [1], it has shown that if a Riemannian manifold admits a non- trivial Riemannian submersion with total geodesic fibers, then it cannot be isometrically immersed in any Riemannian manifold of non-positive sectional curvature as a minimal submanifold. In this paper, we consider a nontrivial Riemannian submersion and investigate some properties on Lagrangian iso- metric immersions using the submersion invariant.