Global symplectic coordinates on gradient K?hler-Ricci solitons

摘要

A classical result of McDuff [14] asserts that a simply connected complete K?hler manifold (M, g, ω) with non positive sectional curvature admits global symplectic coordinates through a symplectomorphism Ψ: M → ?~(2n) (where n is the complex dimension of M), satisfying the following property (proved by E. Ciriza in [4]): the image Ψ(T) of any complex totally geodesic submanifold T ? M through the point p such that Ψ(p) = 0, is a complex linear subspace of ?~n ? ?~(2n). The aim of this paper is to exhibit, for all positive integers n, examples of n-dimensional complete K?hler manifolds with non-negative sectional curvature globally symplectomorphic to ?2n through a symplectomorphism satisfying Ciriza's property.