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arXiv 1703.06646math.MG
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与$\SOL$几何中平移曲线相关的三角角和

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

Jenő Szirmai

摘要:

在研究了$\NIL$和$\SLR$几何中的测地三角形和平移三角形及其角和之后,我们考虑了三维Thurston几何之一的$\SOL$空间中的类似问题.分析了$\SOL$几何中平移三角形的内角和,证明了内角和可以大于或等于$π$ .在我们的工作中,我们将使用由E. \cite{M97}中的Molnár,

英文摘要:

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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