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Covariant symplectic structure of the complex Monge-Ampère equation | | Y. Nutku
; | | Date: |
24 Apr 2000 | | Journal: | Phys.Lett. A268 (2000) 293 | | Subject: | hep-th gr-qc | | Abstract: | The complex Monge-Ampère equation admits covariant bi-symplectic structure for complex dimension 3, or higher. The first symplectic 2-form is obtained from a new variational formulation of complex Monge- Ampère equation in the framework of the covariant Witten-Zuckerman approach to symplectic structure. We base our considerations on a reformulation of the Witten-Zuckerman theory in terms of holomorphic differential forms. The first closed and conserved Witten-Zuckerman symplectic 2-form for the complex Monge-Ampère equation is obtained in arbitrary dimension and for all cases elliptic, hyperbolic and homogeneous. The connection of the complex Monge-Ampère equation with Ricci-flat Kähler geometry suggests the use of the Hilbert action. However, we point out that Hilbert’s Lagrangian is a divergence for Kähler metrics. Nevertheless, using the surface terms in the Hilbert Lagrangian we obtain the second Witten-Zuckerman symplectic 2-form for complex dimension>2. | | Source: | arXiv, hep-th/0004164 | | Services: | Forum | Review | PDF | Favorites | |
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