  In the Kerr geometry, we calculate various surfaces of constant curvature
invariants. These extend well beyond the Kerr horizon, and we argue that they
might be of observational significance in connection with non-minimally coupled
matter fields. Moreover, we demonstrate that the principal null directions of
the Kerr geometry can be obtained by projections involving either the
Bel--Robinson or the Kummer tensor. We conjecture that this is also possible in
more general settings.
