  The first order Plebanski formulation of (complex) general relativity (GR) in
terms of self-dual 2-forms admits a generalization, proposed by Krasnov, that
is qualitatively different from other possible generalizations of GR in terms
of metric variables. In this paper, we investigate, within a minimal
modification, and in a perturbative approach, the geometrical meaning of the
field variables used in the Krasnov generalization, and compare them to the
field variables used in the Plebanski formulation.
