Abstract:
We review basic results from Riemannian geometry, and then construct the conformal tractor calculus, a natural calculus for studying this generalisation of Riemannian manifolds. We also illustrate how conformal geometry fits into the more general picture of parabolic geometry, and study some properties of conformal manifolds with boundary. Finally, we look to the theory of BGG equations, and give some results concerning conserved quantities arising from conformal Killing fields and distinguished curves.
