Abstract: The projective transformation of the special semi-symmetric metric recurrent connection is studied in this paper. First of all, an invariant under this transformation is granted; Secondly, by inducing of the invariant and making use of the properties that the corresponding covariant derivative keeps being fixed under the distinctness connection, the curvature tensor expression of the Riemannian manifold is posed at the same time.

Key words:  projective , transformation;semi-symmetric , metric , connection;metric , recurrent connection;invariant;curvature ,  tensor ,  , expression;covariant ,  , derivative