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Moreover, we show that the $G$-orbits in $\\RR^n_s$ are affinely diffeomorphic to $G$ endowed with the (0)-connection. If the induced metric on the $G$-orbits is non-degenerate, then $G$ (and hence $\\Gamma$) has linear abelian holonomy. If additionally $G$ is not abelian, then $G$ contains a certain subgroup of dimension 6. 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We show that $M$ is a trivial fiber bundle $G/\\Gamma\\to M\\to\\RR^{n-k}$, where $G$ is the Zariski closure of $\\Gamma$ in $\\Iso(\\RR^n_s)$. Moreover, we show that the $G$-orbits in $\\RR^n_s$ are affinely diffeomorphic to $G$ endowed with the (0)-connection. If the induced metric on the $G$-orbits is non-degenerate, then $G$ (and hence $\\Gamma$) has linear abelian holonomy. If additionally $G$ is not abelian, then $G$ contains a certain subgroup of dimension 6. 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