In a previous work, the hyperbolic conformality for bicomplex functions was introduced, and it was proved that, with the adequate hypothesis, a bicomplex holomorphic function is hyperbolic conformal. The aim of this paper is to extend this idea to ${𝔻}^n$, with $𝔻$ the set of hyperbolic numbers. Thus, the fundaments of the analysis in ${𝔻}^n$ are presented here, as well as the generalization of some geometric hyperbolic objects that were defined in the context of bicomplex analysis.

中文翻译：

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多维双曲空间中的双曲保形

在之前的工作中，引入了双复函数的双曲共形，并证明了在适当的假设下，双复全纯函数是双曲共形的。本文的目的是将这个想法扩展到${𝔻}^n$， 和$𝔻$双曲数的集合。因此，分析的基础${𝔻}^n$这里介绍了一些几何双曲对象的概括，这些对象是在双复分析的上下文中定义的。