Symplectic Duality of Symmetric Spaces

2006/03/06 by Loi, Antonio J. Di Scala Andrea · 1 citation
#53D05 #58F06 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.math/0603141

Abstract

With the aid of the theory of Jordan triple systems, we construct an explicit bi-symplectomorphism between a Hermitian symmetric space of non-compact type and \Cⁿ equipped with both the flat Kaehler-form and the Fubini-Study form. Our symplectomorphism is an explicit version of the symplectomorphism between Kaehler manifolds with non positive radial curvature and \Cⁿ, whose existence was proved by Dusa McDuff. As a byproduct we get an interesting characterization of the Bergman form on a Hermitian space in terms of its restriction to classical Hermitian symmetric spaces of noncompact type.

Cited by

• On the Bergman metric of Cartan-Hartogs domains

Related

• On symplectic geometry of tangent bundles of Hermitian symmetric spaces
• Kähler duality and projective embeddings
• Symplectic Symmetric Spaces
• Kaehler spaces, nilpotent orbits, and singular reduction
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