Complete invariant Kähler metrics on cotangent bundles of spheres

Анотація

For the spheres Sⁿ=SO(n + 1)/SO(n), n≥3 , all complete SO(n+1)-invariant Kähler metrics g with the canonical symplectic form as the Kähler form on the cotangent bundle T*Sⁿ are described. This description of the corresponding Kähler structure (J, g) (with the complex structure J) is based on the methods of sym¬metric Lie algebra theory. We consider also analogical complete Kähler structures (J, g) which are invariant with respect to the normalized geodesic flow on the punctured cotangent bundle T*Sⁿ\Sⁿ.