CR structures and general relativity
Prof. Denson C. Hill
1. Brief introduction to several complex variables.
2. Brief introduction to CR stuctures on manifolds.
3. Brief introduction to Einstein's equations in
general relativity. Shear free congruences of
null geodesics in 4-dim Lorentzian spacetimes.
4. Connection with the local embedding problem for
3-dim CR structures.
5. The intrinsic geometry of 3-dim congruences.
6. The Goldberg-Sachs theorem in a 4-dim spacetime,
it's analogues in other signatures, and it's
generalizations.