The Killing fields of the two-sphere S^2, or more generally the n-sphere S^n should be obvious from ordinary intuition: spheres, having rotational symmetry, should possess Killing fields which generate rotations about any axis. That is, we expect S^2 to have symmetry under the action of the 3D rotation group SO(3). That is, by using the a priori knowledge that spheres can be embedded in Euclidean space, it is immediately possible to guess the form of the Killing fields. This is not possible in general, and so this example is of very limited educational value.
