Kahler structures on the tangent bundles of rank-one symmetric spaces

For rank-one Riemannian symmetric spaces , , with semisimple Lie groups  all -invariant Kahler structures on subdomains of the symplectic manifolds are constructed. It is shown that this class of Kahler structures is stable under the reduction procedure. A Lie algebraic method of description of -invariant Kahler structures on the tangent bundles of symmetric spaces is presented. Related questions of the description of the Lie triple system of the space in terms of its spinor structure are also discussed.