On a Riemannian manifold there are a good number of orthogonal invariants
that one may use to investigate its homogeniety.  These are known as Weyl
Invariants, and it has been shown by Prufer, Tricerri and Vanhecke in
1996 that if enough of these Weyl Invariants
are constant (depending on the dimension of the manifold) then the
manifold in question is homogeneous and classified up to isometry by these
constants.

In the higher signature setting this theorem is false,
demonstrating a need for more invariants in this case.  I will present
several counterexamples and derive alternative invariants of the
underlying algebraic structures of these manifolds.