Nayatani's metric and conformal transformations of a Kleinian manifold

According to Schoen and Yau (1988), an extensive class of conformally flat manifolds is realized as Kleinian manifolds. Nayatani (1997) constructed a metric on a Kleinian manifold $M$ which is compatible with the canonical flat conformal structure. He showed that this metric $g_N$ has a large symmetry if $g_N$ is a complete metric. Under certain assumptions including the completeness of $g_N$, the isometry group of $(M,g_N)$ coincides with the conformal transformation group of $M$. In this paper, we show that $g_N$ may have a large symmetry even if $g_N$ is not complete. In particular, every conformal transformation is an isometry when $(M,g_N)$ corresponds to a geometrically finite Kleinian group.