Kaluza-Klein or fibre bundles?
Killing's equations in dimension two and systems of finite type
A PDE system is said to be of finite type if all possible derivatives at some order can be solved for in terms lower order derivatives. An algorithm for determining whether a system of finite type has solutions is outlined. The results are then applied to the problem of characterizing symmetric linear connections in two dimensions that possess homogeneous linear and quadratic integrals of motions, that is, solving Killing's equations of degree one and two.
Kinematic geometry of triangles and the study of the three-body problem.