  The manifold under consideration consists of the faithful normal states on a
sigma-finite von Neumann algebra in standard form. Tangent planes and
approximate tangent planes are discussed. A relative entropy/divergence
function is assumed to be given. It is used to generalize the notion of an
exponential arc connecting one state to another. The generator of the
exponential arc is shown to be unique up to an additive constant. In the case
of Araki's relative entropy every selfadjoint element of the von Neumann
algebra generates an exponential arc. The generators of composed exponential
arcs are shown to add up. The metric derived from Araki's relative entropy is
shown to reproduce the Kubo-Mori metric. The latter is the metric used in
Linear Response Theory. The e- and m-connections describe a dual pair of
geometries. Any finite number of linearly independent generators determines a
submanifold of states connected to a given reference state. Such a submanifold
is a quantum generalization of a dually flat statistical manifold.
