  A Cartan manifold is a smooth manifold M whose slit cotangent bundle T*M0 is
endowed with a regular Hamiltonian K which is positively homogeneous of degree
2 in momenta. The Hamiltonian K defines a (pseudo)-Riemannian metric gij in the
vertical bundle over T*M0 and using it a Sasaki type metric on T*M0 is
constructed. A natural almost complex structure is also defined by K on T*M0 in
such a way that pairing it with the Sasaki type metric an almost K\"ahler
structure is obtained. In this paper we deform gij to a pseudo-Riemannian
metric Gij and we define a corresponding almost complex K\"ahler structure. We
determine the Levi-Civita connection of G and compute all the components of its
curvature. Then we prove that if the structure (T*M0, G, J) is K\"ahler-
Einstein, then the Cartan structure given by K reduce to a Riemannian one.
