# Problem Sheet V

This Problem Sheet is based on Lectures 48, 49, and 50.

- Problem 1 is shows that isometries are volume-preserving, but that the converse can fail.
- Problem 2 is the
*Divergence Theorem* - Problem 3 introduces the
*curl* - Problem 4 shows that Einstein metrics only become interesting in dimensions at least 4.
- Problem 5 computes the geodesic flow in terms of Jacobi fields.
- Problem 6 is about
*higher order covariant derivatives*.

Comments and questions?