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A classical result of D. McDuff asserts that a simply-connected completeKaehler manifold $(M,g,\omega)$ with non positive sectional curvature admitsglobal symplectic coordinates through a symplectomorphism $\Psi: M\rightarrowR^{2n}$ (where $n$ is the complex dimension of $M$), satisfying the followingproperty (proved by E. Ciriza): the image $\Psi (T)$ of any complex totallygeodesic submanifold $T\subset M$ through the point $p$ such that $\Psi(p)=0$,is a complex linear subspace of $C^n \simeq R^{2n}$. The aim of this paper isto exhibit, for all positive integers $n$, examples of $n$-dimensional completeKaehler manifolds with non-negative sectional curvature globallysymplectomorphic to $R^{2n}$ through a symplectomorphism satisfying Ciriza'sproperty.

Global symplectic coordinates on gradient Kaehler-Ricci solitons