Is the Nother symmetric approach consistent with the dynamical equation innon-minimal scalar-tensor theories?

The form of the coupling of the scalar field with gravity and the potential have been found by applying the Nother theorem to two-dimensional minisupe rspaces in an induced gravity model. It has been observed that though the f orms thus obtained are consistent with all the equations pound (X) L = 0, y et they do not satisfy the field equations for k = +/-1 in the Robertson-Wa lker model. It has been pointed out that this is not due to the degeneracy of the Lagrangian, since this problem does not appear in the k = 0 case. It has also been shown that though the Nother theorem fails to extract any sy mmetry from the Lagrangian of such a model for k = +/-1, symmetry exists, w hich can easily be found by studying the continuity equation.