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NAYATANI’S METRIC AND CONFORMAL TRANSFORMATIONS OF A KLEINIAN Manifold

By Yasuhiro Yabuki

Abstract

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 gN has a large symmetry if gN is a complete metric. Under certain assumptions including the completeness of gN, the isometry group of (M,gN) coincides with the conformal transformation group of M. In this paper, we show that gN may have a large symmetry even if gN is not complete. In particular, every conformal transformation is an isometry when (M, gN) corresponds to a geometrically finite Kleinian group

Year: 2007
OAI identifier: oai:CiteSeerX.psu:10.1.1.309.1919
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