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

zbMath1451.53024arXiv1906.04037MaRDI QIDQ4971462

Jenő Szirmai

Publication date: 12 October 2020

Full work available at URL: https://arxiv.org/abs/1906.04037

zbMATH Keywords

Thurston geometriesgeodesic trianglesinterior angle sum\(\mathbf S^2 \times \mathbb R\), \(\mathbf H^2 \times \mathbb R\) geometries

Mathematics Subject Classification ID

Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Non-Euclidean differential geometry (53A35) Local Riemannian geometry (53B20) Projective differential geometry (53A20) Other geometric structures on 3-manifolds (57K35)

Related Items (3)

Fibre-like cylinders, their packings and coverings in \(\widetilde{\mathbf{SL}_2 \mathbf{R}}\) space ⋮ Translation-like isoptic surfaces and angle sums of translation triangles in \(\mathbf{Nil}\) geometry ⋮ Isoptic surfaces of segments in \(\mathbf{S}^2 \times \mathbf{R}\) and \(\mathbf{H}^2 \times \mathbf{R}\) geometries

Cites Work

• A candidate for the densest packing with equal balls in Thurston geometries
• Geodesic ball packings in \(S^{2} \times R\) space for generalized Coxeter space groups
• Simply transitive geodesic ball packings to \(\mathbf{S}^2\times \mathbf{R}\) space groups generated by glide reflections
• The densest translation ball packing by fundamental lattices in Sol space
• Curvatures of left invariant metrics on Lie groups
• The projective interpretation of the eight 3-dimensional homogeneous geometries
• Bisector surfaces and circumscribed spheres of tetrahedra derived by translation curves in \textbf{Sol} geometry
• Nil geodesic triangles and their interior angle sums
• Projective metric realizations of cone-manifolds with singularities along 2-bridge knots and links
• The sum of the interior angles in geodesic and translation triangles of Sl2(R)~ geometry
• The Geometries of 3-Manifolds
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