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Nayatani's metric and conformal transformations of a Kleinian manifold
Author(s):
Yasuhiro
Yabuki
Journal:
Proc. Amer. Math. Soc.
136
(2008),
301-310.
MSC (2000):
Primary 53A30;
Secondary 22E40
Posted:
October 5, 2007
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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  which is compatible with the canonical flat conformal structure. He showed that this metric  has a large symmetry if  is a complete metric. Under certain assumptions including the completeness of  , the isometry group of  coincides with the conformal transformation group of  . In this paper, we show that  may have a large symmetry even if  is not complete. In particular, every conformal transformation is an isometry when  corresponds to a geometrically finite Kleinian group.
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Additional Information:
Yasuhiro
Yabuki
Affiliation:
Mathematical Institute, Tohoku University, 980-8578 Sendai, Japan
Email:
sa3m30@math.tohoku.ac.jp
DOI:
10.1090/S0002-9939-07-09022-3
PII:
S 0002-9939(07)09022-3
Keywords:
Nayatani's metric,
geometrically finite,
conformally flat.
Received by editor(s):
June 15, 2006
Received by editor(s) in revised form:
November 24, 2006
Posted:
October 5, 2007
Communicated by:
Richard A. Wentworth
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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