BooksirmaCollected Volumepp. 321–409

Spherical, hyperbolic, and other projective geometries: convexity, duality, transitions

  • François Fillastre

    Université de Cergy-Pontoise, France
  • Andrea Seppi

    Université du Luxembourg, Esch-sur-Alzette, Luxembourg
Spherical, hyperbolic, and other projective geometries: convexity, duality, transitions cover
Download Chapter PDF

A subscription is required to access this book chapter.

Abstract

We give an elementary projective geometry presentation of the classical Riemannian model spaces (elliptic and hyperbolic spaces) and of the classical Lorentzian model spaces (de Sitter and anti-de Sitter spaces). We also present some relevant degenerate model spaces (Euclidean and co-Euclidean spaces, Lorentzian Minkowski and co-Minkowski spaces), and geometric transitions. An emphasis is given to dimensions 2 and 3, convex subsets, duality, and geometric transitions between the spaces.