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Descripción
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| The space of symplectic connections on a symplectic manifold is a symplectic affine space. M. Cahen and S. Gutt showed that the action of the group of Hamiltonian diffeomorphisms on this space is Hamiltonian and calculated the moment map. This is analogous to, but distinct from, the action of Hamiltonian diffeomorphisms on the space of compatible almost complex structures that motivates study of extremal Kähler metrics. In particular, moment constant connections are critical, where a symplectic connection is critical if it is critical, with respect to arbitrary variations, for the L2-norm of the Cahen?Gutt moment map. This occurs if and only if the Hamiltonian vector field generated by its moment map image is an infinitesimal automorphism of the symplectic connection. This paper develops the study of moment constant and critical symplectic connections, following, to the extent possible, the analogy with the similar, but different, setting of constant scalar curvature and extremal Kähler metrics. | |
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Internacional
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Si |
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JCR del ISI
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Si |
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Título de la revista
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Journal of Symplectic Geometry |
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ISSN
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1527-5256 |
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Factor de impacto JCR
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0,985 |
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Información de impacto
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JCR 2018. 96/314 en Mathematics (Q2) |
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Volumen
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17 |
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DOI
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10.4310/JSG.2019.v17.n6.a4 |
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Número de revista
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6 |
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1683 |
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1771 |
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