A symmetry for vanishing cosmological constant in an extra-dimensional toy model

We introduce a symmetry principle that forbids a bulk cosmological constant in six and ten dimensions. Then the symmetry is extended in six dimensions so that it insures absence of 4-dimensional cosmological constant induced by the six-dimensional curvature scalar, at least, for a class of metrics. A small cosmological constant may be induced in this scheme by breaking of the symmetry by a small amount.