RIEMANNIAN SUBMERSIONS FROM FRAMED METRIC MANIFOLDS

In this paper, we first define the concept of framed submersions between framed metric manifolds, then we provide an example and show that the vertical and horizontal distributions of such submersions are invariant with respect to the framed metric structure of the total manifold. Moreover, we obtain various properties of the O'Neill's tensors for such submersions and find the integrability of the horizontal distribution. We also find necessary and sufficient conditions for a framed submersion to be totally geodesic. The study is focused on fundamental properties and the transference of structures defined on the total manifold.