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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, gN ) corresponds to a geometrically finite Kleinian group.

Nayatani’s metric and conformal transformations of a Kleinian manifold