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## Interior angle sums of geodesic triangles in S2XR and H2XR geometries

Authors: Jenö Szirmai

### Abstract

In the present paper we study $\SXR$ and $\HXR$ geometries, which are homogeneous Thurston 3-geometries. We analyse the interior angle sums of geodesic triangles in both geometries and we prove that in $\SXR$ space it can be larger than or equal to $\pi$ and in $\HXR$ 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 $\SXR$ and $\HXR$ geometries described by E. Moln\'ar in \cite{M97}.

Budapest University of Technology and
Economics Institute of Mathematics,
Department of Geometry,
Budapest, P. O. Box: 91, H-1521
E-mail:

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