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arXiv · 2010.05854

Symplectic geometry of Cartan-Hartogs domains

Roberto Mossa·Michela Zedda
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Abstract

This paper studies the geometry of Cartan-Hartogs domains from the symplectic point of view. Inspired by duality between compact and noncompact Hermitian symmetric spaces, we construct a dual counterpart of Cartan-Hartogs domains and give explicit expression of global Darboux coordinates for both Cartan-Hartogs and their dual. Further, we compute their symplectic capacity and show that a Cartan-Hartogs admits a symplectic duality if and only if it reduces to be a complex hyperbolic space.

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Roberto Mossa, Michela Zedda. 2020-10-12. Symplectic geometry of Cartan-Hartogs domains. https://doi.org/10.1007/s10231-022-01201-1

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