Complete invariant Kähler metrics on cotangent bundles of spheres

I. V. Mykytyuk


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.

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