Geodesic
Interior angle sums of geodesic triangles in $\mathbf{S^2}\times\mathbf{R}$ and $\mathbf{H^2}\times\mathbf{R}$ geometries
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2020), pp. 44-61.

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In the present paper we study $\mathbf{S^2}\times\mathbf{R}$ and $\mathbf{H^2}\times\mathbf{R}$ geometries, which are homogeneous Thurston $3$-geometries. We analyse the interior angle sums of geodesic triangles in both geometries and we prove that in $\mathbf{S^2}\times\mathbf{R}$ space it can be larger than or equal to $\pi$ and in $\mathbf{H^2}\times\mathbf{R}$ space the angle sums can be less than or equal to $\pi$. This proof is a new direct approach to the issue and it is based on the projective model of $\mathbf{S^2}\times\mathbf{R}$ and $\mathbf{H^2}\times\mathbf{R}$ geometries described by E. Molnár in [7]. 
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     title = {Interior angle sums of geodesic triangles in $\mathbf{S^2}\times\mathbf{R}$ and $\mathbf{H^2}\times\mathbf{R}$ geometries},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
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Jenő Szirmai. Interior angle sums of geodesic triangles in $\mathbf{S^2}\times\mathbf{R}$ and $\mathbf{H^2}\times\mathbf{R}$ geometries. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2020), pp. 44-61. http://geodesic.mathdoc.fr/item/BASM_2020_2_a4/

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