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<p>In the present paper, we deal with non-constant curvature Thurston geometries [<CitationRef AdditionalCitationIDS="CR2 CR3" CitationID="CR1">1</CitationRef>–<CitationRef CitationID="CR4">4</CitationRef>]. We define and determine the generalized translation-like Apollonius surfaces and thus also bisector surfaces as a special case. Moreover, we give a possible definition of the “surface of a translation-like triangle” in each investigated geometry. In our work, we will use the projective model of Thurston geometries described by E. Molnár in [<CitationRef CitationID="CR1">1</CitationRef>].</p>

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Translation-like Apollonius and Triangular Surfaces in Non-constant Curvature Thurston Geometries

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月30日

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  • Géza Csima,
  • Jenő Szirmai

摘要

In the present paper, we deal with non-constant curvature Thurston geometries [1–4]. We define and determine the generalized translation-like Apollonius surfaces and thus also bisector surfaces as a special case. Moreover, we give a possible definition of the “surface of a translation-like triangle” in each investigated geometry. In our work, we will use the projective model of Thurston geometries described by E. Molnár in [1].