A Kähler structure on the punctured cotangent bundle of complex and quaternion projective spaces and its application to a geometric quantization. I (Q1894177)

The authors consider the punctured cotangent bundle \(T^*_0 P^n\mathbb{C}\) (resp. \(T^*_0 P^n \mathbb{H})\) of the complex (resp. quaternion) projective space \(P^n\mathbb{C}\) (resp. \(P^n \mathbb{H}\)) and prove that the bundle space admits a Kählerian structure whose Kähler form coincides with the symplectic form, just like in the case of the spheres. The authors also describe the automorphisms of \(T^*_0 P^n\mathbb{C}\) and \(T^*_0 P^n H\). The arguments are based on the diagonalization of the geodesic flows.