Translation-like Apollonius and triangular surfaces in non-constant curvature Thurston geometries

2024/10/30 by Géza Csima, Csima, Géza, Jenő Szirmai +1 · 2 citations
Mathematics · #Mathematical Dynamics and Fractals #Geometric Analysis and Curvature Flows #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2410.22955

Abstract

In the present paper we deal with non-constant curvature Thurston geometries \citeM97, \citeS, \citeSz22-3,\citeW06. We define and determine the generalized trans\-lation-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 \citeM97.

Cited by

• Lattice-like Packings and Coverings with Congruent Translation Balls and Cylinders in Sol geometry
• Menelaus' and Ceva's theorems for translation triangles in Thurston geometries

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• Classical Notions and Problems in Thurston Geometries