The sum of the interior angles in geodesic and translation triangles of Sl2(R) geometry

TL;DR

This paper investigates the interior angle sums of translation and geodesic triangles in the universal cover of Sl2(R) geometry, revealing that translation triangles always have angle sums exceeding pi, while geodesic triangles can vary.

Contribution

It provides new insights into the angle sum properties of triangles in Sl2(R) geometry, distinguishing between translation and geodesic triangles.

Findings

Translation triangles have angle sums greater than pi.

Geodesic triangles can have angle sums greater than, equal to, or less than pi.

Abstract

We study the interior angle sums of translation and geodesic triangles in the universal cover of Sl2(R) geometry. We prove that the angle sum is larger then pi for translation triangles and for geodesic triangles the angle sum can be larger, equal or lessthan \pi.