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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$ 3$-manifolds with positive flat conformal structure


Authors: Reiko Aiyama and Kazuo Akutagawa
Journal: Proc. Amer. Math. Soc. 140 (2012), 3587-3592
MSC (2010): Primary 53A30, 53C21; Secondary 57M10
Published electronically: February 15, 2012
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Abstract: In this paper, we consider a closed $ 3$-manifold $ M$ with flat conformal structure $ C$. We will prove that if the Yamabe constant of $ (M, C)$ is positive, then $ (M, C)$ is Kleinian.


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Additional Information

Reiko Aiyama
Affiliation: Department of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan
Email: aiyama@math.tsukuba.ac.jp

Kazuo Akutagawa
Affiliation: Division of Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
Email: akutagawa@math.is.tohoku.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11423-6
PII: S 0002-9939(2012)11423-6
Keywords: Differential geometry, geometric topology
Received by editor(s): April 5, 2011
Published electronically: February 15, 2012
Additional Notes: The second author was supported in part by the Grants-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, No. 21540097.
Communicated by: Lei Ni
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.