Second Natural Connection on Riemannian Π-Manifolds

An object of investigation is the differential geometry Riemannian Π-manifolds; in particular, a natural connection, determined by property its torsion tensor, defined, and it called second connection on Π-manifold. The uniqueness this proved, necessary sufficient condition for coincidence with known first considered manifolds found. form tensor obtained classes Π-manifolds, which differs from connection. All main are characterized respect to explicit example dimension 5 given support proven assertions.