Eighteen Essays in Non-Euclidean Geometry

Vincent Alberge (1) , Athanase Papadopoulos (2)

1 Fordham University [New York]
2 IRMA - Institut de Recherche Mathématique Avancée

This book consists of a series of self-contained essays on non-Euclidean geometry in a broad sense, including the classical geometries of constant curvature (spherical and hyperbolic), de Sitter, anti-de Sitter, co-Euclidean, co-Minkowski geometries, Hermitian geometry, and some axiomatically defined geometries. Some of these essays deal with very classical questions and others address problems that are at the heart of present day research, but all of them are concerned with fundamental topics.

Mots clés: Non-Euclidean geometry; spherical geometry; hyperbolic geometry; Busemann type geometry; curvature; geographical map; non-euclidean area; non-euclidean volume; Brahmagupta’s formula; Ptolemy’s theorem; Casey’s theorem; Sforza’s formula; Seidel’s problem; infinitesimal rigidity; static rigidity; Pogorelov map; Maxwell–Cremona correspondence; exterior hyperbolic geometry; de Sitter geometry; non-Euclidean conics; bifocal properties; focus-directrix properties; pencils of conics; projective geometry; convexity; duality; transition; Hermitian trigonometry; complex projective trigonometry; shape invariant; metric plane projective-metric plane

Domaines: Géométrie différentielle [math.DG]; Topologie géométrique [math.GT]; Géométrie métrique [math.MG]; Histoire et perspectives sur les mathématiques [math.HO]

Vincent Alberge, Athanase Papadopoulos (Dir.). Eighteen Essays in Non-Euclidean Geometry. 2019, European Mathematical Soiety Publishing House, Zurich, 475 p., 978-3-03719-196-5. ⟨10.4171/196⟩. ⟨hal-02126617⟩