17 June 2019 Mon 13:15-14:45 REALF A010

Rod Gover (University of Auckland)

"An introduction to conformal and projective tractor calculus".

From a Riemannian manifold (M,g), a conformal geometry arises if we retain only the equivalence class [g] of metrics that agree with g up to multiplication by some positive function f ; (M,[g]) is "less rigid" than (M,g) in the sense that it has a notion of angle but not length. Similarly a projective geometry consists of a manifold equipped with an equivalence class of torsion-free affine connections where the equivalence relation is that two connections are related if they have the same unparametrised geodesics. I will give an introduction to the construction of the basic invariant calculus for conformal and projective differential geometry.