Abstract
A Cartan manifold is a smooth manifold M whose slit cotangent bundle 0 * M T is endowed with a regular Hamiltonian K which is positively homogeneous of degree 2 in momenta. The Hamiltonian K defines a (pseudo)-Riemannian metric ij g in the vertical bundle over 0 * M T and using it, a Sasaki type metric on 0 * M T is constructed. A natural almost complex structure is also defined by K on 0 * M T in such a way that pairing it with the Sasaki type metric an almost Kahler structure is obtained. In this paper we deform ij g to a pseudo-Riemannian metric ij G and we define a corresponding almost complex Kahler structure. We determine the Levi-Civita connection of G and compute all the components of its curvature. Then we prove that if the structure
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