  In our previous paper (I) we derived information geometric objects from the
two parameter generalized entropy of Hanel and Thurner (2011), using the c,d
parameters as labels of the corresponding manifolds. Here we follow a
completely different approach by considering these parameters as coordinates of
our information manifolds. This gives a manageable two-dimensional manifold
amenable to easy manipulations but most importantly it offers a direct
characterization of complex systems in terms of the pair of the c,d values. As
a result we obtain certain characteristic values from the scalar curvature
which we could conjecture that they represent complex systems with specific
behavior. It is further observed that the boundary values of the c,d parameters
which characterize the Hanel-Thurner classification are in some sense singular.
This asks for a regularization scheme which we try to establish.
