2023/02/15 by Géza Csima, Csima, Géza, Jenő Szirmai +1
Engineering · Mathematics · #52C35 #53A20 #53A35 #53B20 #Advanced Materials and Mechanics #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2302.07653
openalex publication_date 2023/02/15 · openalex created_date 2023/02/18 · openalex updated_date 2026/07/28
After having investigated the geodesic and translation triangles and their angle sums in \SOL and \SLR geometries we consider the analogous problem in \NIL space that is one of the eight 3-dimensional Thurston geometries. We analyze the interior angle sums of translation triangles in \NIL geometry and we provide a new approach to prove that it can be larger than or equal to π. Moreover, for the first time in non-constant curvature Thurston geometries we have developed a procedure for determining the equations of \NIL isoptic surfaces of translation-like segments and as a special case of this we examine the \NIL translation-like Thales sphere, which we call \it Thaloid. In our work we will use the projective model of \NIL described by E. Molnár in \citeM97.