LORENTZIAN GEOMETRY

Flat Lorentz (3, 1) space is the natural home for Einstein's Special Theory of Relativity, with three "space" dimensions and one "time" dimension. The geometry naturally encodes the ideas of inertial frames, time and space dilation. Much of the mathematical terminology and research interests are infused with physical considerations, but purely mathematical questions are at the core of this treatment.

This is an introduction to Lorentzian (n, 1) geometry for all n ≥ 1, examining the constant curvature spaces: flat, de Sitter (positive curvature) and anti-de Sittter spaces. The conformal boundaries of these Lorentz spacetimes will also be constructed. The connection between Lorentz (2, 1) geometry and geometry of the hyperbolic plane will also be investigated.