The analytic continuation of hyperbolic space

Yunhi Cho; Hyuk Kim

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arXiv · math/0612372

The analytic continuation of hyperbolic space

Yunhi Cho·Hyuk Kim

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Abstract

We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter space as subspaces and which is obtained as an analytic continuation of the hyperbolic space. The construction of the extended space gives rise to a complex valued geometry consistent with both the hyperbolic and de Sitter space. Such a construction shed a light and inspires a new insight for the study of the hyperbolic geometry and Lorentzian geometry. We discuss the advantages of this new geometric model as well as some of its applications.

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BibTeX RIS

Yunhi Cho, Hyuk Kim. 2010-01-05. The analytic continuation of hyperbolic space. https://arxiv.org/abs/math/0612372

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