Invariant Kähler structures on the cotangent bundles of compact symmetric spaces

Abstract

For rank-one symmetric spaces $M$ of the compact type all Kähler structures $F^\lambda$, defined on their punctured tangent bundles $T^0M$ and invariant with respect to the normalized geodesic flow on $T^0M$, are constructed. It is shown that this class $\{F^\lambda \}$ of Kähler structures is stable under the reduction procedure.