Triangle angle sums related to translation curves in $\SOL$ geometry
DOI:
https://doi.org/10.24193/subbmath.2022.3.14Keywords:
Thurston geometries, $\SOL$ geometry, translation and geodesic triangles, interior angle sumAbstract
After having investigated the geodesic and translation triangles and their angle sums in $\NIL$ and $\SLR$ geometries we consider the analogous problem in $\SOL$ space thatis one of the eight 3-dimensional Thurston geometries.
We analyse the interior angle sums of translation triangles in $\SOL$ geometry
and prove that it can be larger or equal than $\pi$.
In our work we will use the projective model of $\SOL$ described by E. Moln\'ar in \cite{M97}.
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