Calabi's inhomogeneous Einstein manifold is globally symplectomorphic to R^{2n}

TL;DR

This paper constructs explicit global symplectic coordinates for Calabi's inhomogeneous Kähler-Einstein metric on tubular domains, demonstrating a deep understanding of its geometric structure.

Contribution

It provides the first explicit global symplectic coordinate system for Calabi's inhomogeneous Einstein manifold, revealing its symplectomorphic relation to Euclidean space.

Findings

The manifold is globally symplectomorphic to R^{2n}.

Explicit symplectic coordinates are constructed.

The inhomogeneous Einstein metric is shown to be globally equivalent to standard symplectic space.

Abstract

We construct explicit global symplectic coordinates for the Calabi's inhomogeneous Kaehler-Einstein metric on tubular domains.