On Geodesic Triangles in Non-Euclidean Geometry
Year: 2024
Type: article
Abstract: In this paper, we study centroids, orthocenters, circumcenters, and incenters of geodesic triangles in non-Euclidean geometry, and we discuss the existence of the Euler line in this context. Moreover, we give simple proofs of the existence of a totally geodesic 2-dimensional submanifold containing a given geodesic triangle in the hyperbolic or spherical 3-dimensional geometry.
Source: Foundations
Authors: Antonella Nannicini, Donato Pertici
Institution: University of Florence
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,137
OpenAlex ID: W4402899031