Equidistant Hypersurfaces Of The Complex Bidisk ${\mathbb{H}}_{\mathbb{C}}^2\times {\mathbb{H}}_{\mathbb{C}}^2$

Abstract

We consider the isometries of the complex hyperbolic bidisk, that is, the product space ${\mathbb{H}}_{\mathbb{C}}^2\times {\mathbb{H}}_{\mathbb{C}}^2$, where each factor ${\mathbb{H}}_{\mathbb{C}}^2$ denotes the complex hyperbolic plane. We investigate the Dirichlet domain formed by the action of a cyclic subgroup $(g_1,g_2)$, where each $g_i$ is loxodromic. We prove that such a Dirichlet domain has two sides.

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