  A natural connection with torsion is defined and it is called the first
natural connection on Riemannian $\Pi$-manifold. Relations between the
introduced connection and the Levi-Civita connection are obtained, as well as
relations between their respective curvature tensors, torsion tensors, Ricci
tensors, and scalar curvatures in the main classes of a classification of
Riemannian $\Pi$-manifolds are presented. An explicit example of dimension 5 is
provided.
