On the volumes of canonical cusps of complex hyperbolic manifolds

Inkang Kim; Joonhyung Kim

doi:10.4134/JKMS.2009.46.3.513

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2009; 46(3): 513-521

Printed May 1, 2009

https://doi.org/10.4134/JKMS.2009.46.3.513

On the volumes of canonical cusps of complex hyperbolic manifolds

Inkang Kim and Joonhyung Kim

Seoul National University

Abstract

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Abstract

We first introduce a complex hyperbolic space and a complex hyperbolic manifold. After defining the canonical horoball and the canonical cusp on the complex hyperbolic manifold, we estimate the volumes of canonical cusps of complex hyperbolic manifolds. Finally, we deal with cusped, complex hyperbolic $2$-manifolds, and in particular, the ones with only one cusp.

Keywords: complex hyperbolic manifold, canonical cusp, Heisenberg isometry

MSC numbers: 22E40, 32Q45, 51M10, 57S30