Symplectic maps of complex domains into complex space forms
Andrea Loi, Fabio Zuddas

TL;DR
This paper provides explicit conditions on Kähler potentials for complex domains to admit symplectic embeddings into complex space forms, including global coordinates, with applications to Ricci-flat metrics like the Taub-NUT metric.
Contribution
It offers explicit criteria for symplectic embeddings of complex domains into space forms based on Kähler potentials, and constructs global symplectic coordinates for Ricci-flat metrics.
Findings
Derived sufficient conditions for symplectic embeddings.
Provided explicit formulas for embeddings in terms of Kähler potentials.
Applied results to Ricci-flat metrics, including Taub-NUT.
Abstract
Let be a complex domain of endowed with a rotation invariant \K form . In this paper we describe sufficient conditions on the \K potential for to admit a symplectic embedding (explicitely described in terms of ) into a complex space form of the same dimension of . In particular we also provide conditions on for 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 constructed by LeBrun (Taub-NUT metric) admits explicitely computable global symplectic coordinates.
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