In this paper we study centroid, orthocenter, circumcenter and incenter for a geodesic triangle 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.
On geodesic triangles in non-Euclidean geometry / Antonella Nannicini; Donato Pertici. - In: FOUNDATIONS. - ISSN 2673-9321. - STAMPA. - 4:(2024), pp. 468-487. [10.3390/foundations4040030]
On geodesic triangles in non-Euclidean geometry
Antonella Nannicini;Donato Pertici
2024
Abstract
In this paper we study centroid, orthocenter, circumcenter and incenter for a geodesic triangle 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.
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