We study non-flat Friedman-Robertson-Walker (FRW) cosmologies searching for Nöther symmetries in the pointlike Lagrangians derived from a general non-minimally coupled gravitational action. The presence of a quadratic coupling makes the dynamics degenerate if the spatial-curvature constant k is different from zero, while exact solutions, through the existence of the symmetry, are found in the minimally coupled case. © 1994 Società Italiana di Fisica.
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