NIL geodesic triangles and their interior angle sums

2016/11/17 by Szirmai, Jenő · 2 citations
#52C35 #53A20 #53A35 #53B20 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1611.05613

Abstract

In this paper we study the interior angle sums of geodesic triangles in \NIL geometry and prove that it can be larger, equal or less than π. We use for the computations the projective model of \NIL introduced by E. Molnár in \citeM97.

Cited by

• Lattice-like Packings and Coverings with Congruent Translation Balls and Cylinders in Sol geometry
• Menelaus' and Ceva's theorems for translation triangles in Thurston geometries

Related

• Triangle angle sums related to translation curves in \SOL geometry
• Interior angle sums of geodesic triangles in S² × R and H² × R geometries
• The sum of the interior angles in geodesic and translation triangles of Sl2(R) geometry
• Interior angle sums of geodesic triangles and translation-like isoptic surfaces in Sol geometry
• On Menelaus' and Ceva's theorems in Nil geometry