  Taking wedge products of the $p$ distinct principal null directions
associated with the eigen-bivectors of the Weyl tensor associated with the
Petrov classification, when linearly independent, one is able to express them
in terms of the eigenvalues governing this decomposition. We study here
algebraic and differential properties of such $p$-forms by completing previous
geometrical results concerning type I spacetimes and extending that analysis to
algebraically special spacetimes with at least 2 distinct principal null
directions. A number of vacuum and nonvacuum spacetimes are examined to
illustrate the general treatment.
