  We analyze the projected effective Einstein equation in a 4-dimensional
arbitrary manifold embedded in a 5-dimensional Riemann-Cartan manifold. The
Israel-Darmois matching conditions are investigated, in the context where the
torsion discontinuity is orthogonal to the brane. Unexpectedly, the presence of
torsion terms in the connection does not modify such conditions whatsoever,
despite of the modification in the extrinsic curvature and in the connection.
Then, by imposing the Z_2-symmetry, the Einstein equation obtained via
Gauss-Codazzi formalism is extended, in order to now encompass the torsion
terms. We also show that the factors involving contorsion change drastically
the effective Einstein equation on the brane, as well as the effective
cosmological constant.
