Triangle angle sums related to translation curves in $\SOL$ geometry

Jenő Szirmai

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arXiv · 1703.06646

Triangle angle sums related to translation curves in $\SOL$ geometry

Jenő Szirmai

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Abstract

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 that is 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 $π$. In our work we will use the projective model of $\SOL$ described by E. Molnár in \cite{M97},

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Jenő Szirmai. 2017-03-20. Triangle angle sums related to translation curves in $\SOL$ geometry. https://arxiv.org/abs/1703.06646

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