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Invariance of the Nayatani metrics for Kleinian manifolds

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Abstract

The Nayatani metric g N is a Riemannian metric on a Kleinian manifold M which is compatible with the standard flat conformal structure. It is known that, for M corresponding to a geometrically finite Kleinian group, g N has large symmetry: the isometry group of (M, g N ) coincides with the conformal transformation group of M. In this paper, we prove that this holds for a larger class of M. In particular, this class contains such M that correspond to Kleinian groups of divergence type.

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Authors and Affiliations

  1. Department of Mathematics, Okayama University, Okayama, 700-8530, Japan

    Katsuhiko Matsuzaki

  2. Mathematical Institute, Tohoku University, Aoba-ku, Sendai, 980-8578, Japan

    Yasuhiro Yabuki

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  1. Katsuhiko Matsuzaki
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  2. Yasuhiro Yabuki
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Correspondence to Yasuhiro Yabuki.

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Matsuzaki, K., Yabuki, Y. Invariance of the Nayatani metrics for Kleinian manifolds. Geom Dedicata 135, 147–155 (2008). https://doi.org/10.1007/s10711-008-9268-7

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  • DOI: https://doi.org/10.1007/s10711-008-9268-7

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