Speaker: Uri Bader (Technion)
Title: What is the Lorentzian analog of the Riemannian sphere?
Abstract: Spheres are the most symmetric compact Riemannian manifolds. A way to formulate the above statement is to consider conformal transformations. The group of conformal transformations of the sphere is non-compact, while the conformal group of any other compact Riemannian manifold is compact (Ferrand, Obata ~70). A Lorentzian manifold is a manifold modelled over the space-time (in the same manner that a Riemannian manifold is a manifold modelled over the space). We will introduce a certain Lorentzian manifold, sometimes called "the boundary of the anti-de-Sitter space", which resembles the symmetric properties of the sphere. We will discuss this resemblance from the point of view of rigidity phenomena occurring for conformal actions of Lie groups on Riemannian and Lorentzian manifolds.