Th   1/12   Lorentzian vector spaces
                  handout 1: Lorentzian vector spaces

Tu   1/17  Hyperquadrics in Minkowski space/ geodesics
                 handout 2: totally geodesic/totally umbilic submanifolds

Th  1/19  Totally geodesic/totally umbilic submanifolds
                 Review: Curvature tensor, jacobi equation, sectional curvature  (Riemannian case)

M   1/23  and W 1/25: sectional curvature of Lorentzian manifolds/ constant curvature and hyperquadrics
                handout 3: sectional curvature of Lorentzian manifolds
                (includes 3 HW problems, due Monday, Feb.6)

M  1/30   Ricci curvature, splitting of the curvature tensor
                handout 4: Ricci curvature, constraints and evolution
                (includes 4 exercises, due Monday, Feb 13)

W 2/1   Constraint and evolution equations; 1st variation of arc length (ref: O'Neill, chapter 10)

M  2/6  Second variation of arc length

W 2/8  The index form: variational meaning, index theorem (statement)

M  2/13   Bonnet-Myers theorem, Rauch comparison thm

W  2/15  Rauch comparison (cont'd), applications

M  2/20  volume growth
               handout 5: volume estimates

W  2/22  volume growth for geodesic spheres

M  2/27  Volume growth: theorems based on Ricci curvature; cut locus

W  2/29   lecture postponed

M   3/5   first variation for hypersurfaces
              handout 7: first and second variation for hypersurfaces
              (version of 3/7)

W  3/7   second variation for hypersurfaces/ focal points ([ON, pp.280-288][dC 10.4]
              problem set

M  3/12  energy-momentum tensor for a relativistic ideal fluid/ Robertson-Walker spacetimes/ skew-product metrics
              (O'Neill: ch. 10 and ch. 7)

W 3/14 skew-product metrics

M 3/19, W 3/21: SPRING BREAK

M 3/26  lecture postponed

W 3/28 RW cosmologies, Friedmann models/ focal points (start)
             handout 8: skew-product metrics, RW cosmological models
             (includes six problems)

M  4/2  causality in Lorentzian manifolds

W  4/4  causality (cont)

M 4/9   Hawking singularity theorem

W  4/11 Schwarzschild solution

M  4/16 Schwarzschild

W  4/18 Schwarzschild
handout 9: Schwarzschild solutions
(preliminary version, 9 problems)
Last  HW set: problems 3,4,5,8(iii),9 (from handout 9)

M  4/23 trapped surfaces and singularities
handout10: trapped surfaces and timelike incompleteness

W  4/25 trapped surfaces and singularities

M  4/30  postponed lecture

W  5/2   postponed lecture