### Monday September 8, 2003

**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.