Riemannian Maps From Kaehler Manifold With Generic Fibers

We study Riemannian maps from almost Hermitian manifolds to Riemannian manifolds for the case when the fibers are genericsubmanifold of the total space. We obtain the integrability conditionsfor the distributions while vertical distribution is always integrable. Wealso study the geometry of the leaves of the distribution which arisefrom such maps, and obtain the necessary and sufficient conditions forthe fibers as well as the total manifold to be generic product manifolds. We, further, obtain the necessary and sufficient condition for aRiemannian maps with generic fibers to be totally geodesic map.