On some connections on locally product Riemannian manifolds - part I

Nevena Pušić

It is a well known fact that a Riemannian metric on a differentible manifold induces a Riemannian metric on its submanifold and, hence, a Riemannian connection on the manifold induces a Riemannian connection on its submanifold. In this paper, we consider the problems in a converse direction and consider five connections from the family of "projective class" on global manifold which can induce a given Riemannian connection on the submanifold. Also, we consider the induced connection on the supplement of the submanifold, if the space is decomposable.