Global symplectic coordinates on complex domains

CUCCU, FABRIZIO;LOI, ANDREA

2006-01-01

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Abstract

In this paper we deal with complex domains M ⊂ Cn equipped with a Ka ̈hler form ω = i ∂∂ ̄f, 2 where f : M → R only depends on |zj|2, j = 1,...,n for the complex coordinates (z1,...,zn) in Cn. We give an explicit symplectic immersion Φ of (M,ω) into R2n in Section 2. In Section 3 we study when the map Φ is a global symplectomorphism for the case of complete Reinhardt domains in C2.