Interior angle sums of geodesic triangles in $S^2\times R$ and $H^2\times R$ geometries

Abstract

In the present paper we study $S^2\times R$ and $H^2\times R$ geometries, which are homogeneous Thurston 3-geometries. We analyse the interior angle sums of geodesic triangles in both geometries and prove, that in $S^2\times R$ space it can be larger or equal than $\pi$ and in $H^2\times R$ space the angle sums can be less or equal than $\pi$. In our work we will use the projective model of $S^2\times R$ and $H^2\times R$ geometries described by E. Molnár in \cite{M97}.

22 pages and 10 figures. arXiv admin note: substantial text overlap with arXiv:1703.06646, arXiv:1611.05613

References in corpus (2)

• Bisector surfaces and circumscribed spheres of tetrahedra derived by translation curves in $\SOL$ geometry
• NIL geodesic triangles and their interior angle sums