Global symplectic coordinates on gradient Kaehler-Ricci solitons

Abstract

A classical result of D. McDuff asserts that a simply-connected complete Kaehler manifold $(M,g,\omega )$ with non positive sectional curvature admits global symplectic coordinates through a symplectomorphism $\Psi :M\to R^{2n}$ (where $n$ is the complex dimension of $M$), satisfying the following property (proved by E. Ciriza): the image $\Psi (T)$ of any complex totally geodesic 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 is to exhibit, for all positive integers $n$, examples of $n$-dimensional complete Kaehler manifolds with non-negative sectional curvature globally symplectomorphic to $R^{2n}$ through a symplectomorphism satisfying Ciriza's property.

8 pages

References in corpus (1)

• Symplectic maps of complex domains into complex space forms

Cited by in corpus (1)

• On Calabi's diastasis function of the cigar metric