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2009•Journal of the Korean Mathematical SocietyOpen access

ON THE VOLUMES OF CANONICAL CUSPS OF COMPLEX HYPERBOLIC MANIFOLDS

Инканг Ким, Joon-Hyung Kim

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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.

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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.

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Available 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.

Key concepts: Mathematics, Cusp (singularity), Hyperbolic manifold, Hyperbolic 3-manifold, Hyperbolic space, Stable manifold, Manifold (fluid mechanics), Hyperbolic equilibrium point

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