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http://dx.doi.org/10.4134/JKMS.2012.49.2.343

ON THE CANONICAL CUSPS IN COMPLEX HYPERBOLIC SURFACES  

Kim, Joon-Hyung (Department of Mathematics Konkuk University)
Publication Information
Journal of the Korean Mathematical Society / v.49, no.2, 2012 , pp. 343-356 More about this Journal
Abstract
In this paper, we consider the canonical cusps in complex hyperbolic surfaces. We will classify canonical cusps in complex hyper-bolic surfaces and find correspondence between them and 3-dimensiona nilpotent groups. This paper is a sequel of our paper [6].
Keywords
complex hyperbolic manifold; canonical cusp; Heisenberg group; Heisenberg infranilmanifold;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
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1 I. Kim and J. Kim, On the volumes of canonical cusps of complex hyperbolic manifolds, J. Korean Math. Soc. 46 (2009), no. 3, 513-521.   DOI   ScienceOn
2 B. Maskit, Kleinian Groups, Grundlehren der Mathematischen Wissenschaften, 287. Springer-Verlag, Berlin, 1988.
3 D. B. McReynolds, Peripheral separebility and cusps of arithemetic hyperbolic orbifolds, Algebr. Geom. Topol. 4 (2004), 721-755.   DOI
4 J. R. Parker, On the volumes of cusped, complex hyperbolic manifolds and orbifolds, Duke Math. J. 94 (1998), no. 3, 433-464.   DOI
5 P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), no. 5, 401-487.   DOI
6 W. Thurston, The geometry and topology of 3-manifolds, preprint, 1991.
7 K. Dekimpe, Almost-Bieberbach Groups: Affine and Polynomial Structures, Lecture Notes in Mathematics, 1639. Springer-Verlag, Berlin, 1996.
8 W. M. Goldman, Complex Hyperbolic Geometry, Oxford Univ. Press, 1999.
9 S. Hersonsky and F. Paulin, On the volumes of complex hyperbolic manifolds, Duke Math. J. 84 (1996), no. 3, 719-737.   DOI
10 J.-M. Hwang, On the volumes of complex hyperbolic manifolds with cusps, Internat. J. Math. 15 (2004), no. 6, 567-572.   DOI   ScienceOn
11 Y. Kamishima, Nonexistence of cusp cross-section of one-cusped complete complex hyperbolic manifolds II, Int. Math. Forum 2 (2007), no. 25-28, 1251-1258.