  A three-dimensional Riemannian manifold has locally 6, 4, 3, 2, 1 or none
independent Killing vectors. We present an explicit algorithm for computing
dimension of the infinitesimal isometry algebra. It branches according to the
values of curvature invariants. These are relative differential invariants
computed via curvature, but they are not scalar polynomial Weyl invariants. We
compare our obstructions to the existence of Killing vectors with the known
existence criteria due to Singer, Kerr and others.
