Symplectic maps of complex domains into complex space forms

Abstract

Let $M\subset{\complex}^n$ be a complex domain of ${\complex}^n$ endowed with a rotation invariant \K form ${\omega }_{\Phi }=\frac{i}{2}\partial \bar{\partial }\Phi$. In this paper we describe sufficient conditions on the \K potential $\Phi$ for $(M,{\omega }_{\Phi })$ to admit a symplectic embedding (explicitely described in terms of $\Phi$) into a complex space form of the same dimension of $M$. In particular we also provide conditions on $\Phi$ for $(M,{\omega }_{\Phi })$ to admit global symplectic coordinates. As an application of our results we prove that each of the Ricci flat (but not flat) \K forms on ${\complex}^2$ constructed by LeBrun (Taub-NUT metric) admits explicitely computable global symplectic coordinates.

to appear in Journal of Geometry and Physics

Cited by in corpus (5)

• Riemannian geometry of Hartogs domains
• Symplectic duality between complex domains
• Calabi's inhomogeneous Einstein manifold is globally symplectomorphic to R^{2n}
• Some remarks on the Kaehler geometry of LeBrun's Ricci flat metrics on C^2
• Some remarks on the symplectic and Kaehler geometry of toric varieties