Braneworld remarks in Riemann-Cartan manifolds

We analyze the projected effective Einstein equation in a four-dimensional arbitrary manifold embedded in a five-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 the modification in the extrinsic curvature and 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.