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

For rank-one Riemannian symmetric spaces $G/K$, $\operatorname{dim}G/K\geqslant3$, with semisimple Lie groups $G$ all $G$-invariant Kahler structures $F$ on subdomains of the symplectic manifolds $T(G/K)$ are constructed. It is shown that this class $\{F\}$ of Kahler structures is stable under the reduction procedure. A Lie algebraic method of description of $G$-invariant Kahler structures on the tangent bundles of symmetric spaces $G/K$ is presented. Related questions of the description of the Lie triple system of the space $F_4/\operatorname{Spin}(9)$ in terms of its spinor structure are also discussed.