Riemannian Maps From Kaehler Manifold With Generic Fibers

Abstract

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