### Symplectic topology and hamiltonian dynamics

I. Ekeland, H. Hofer (1987-1988)

Séminaire Équations aux dérivées partielles (Polytechnique)

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I. Ekeland, H. Hofer (1987-1988)

Séminaire Équations aux dérivées partielles (Polytechnique)

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L. Polterovich (1996)

Geometric and functional analysis

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Bekka, M.B., Neuhauser, M. (2002)

Journal of Lie Theory

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Svatopluk Krýsl (2012)

Commentationes Mathematicae Universitatis Carolinae

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Let $(M,\omega )$ be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection $\nabla $. Symplectic Killing spinor fields for this structure are sections of the symplectic spinor bundle satisfying a certain first order partial differential equation and they are the main object of this paper. We derive a necessary condition which has to be satisfied by a symplectic Killing spinor field. Using this condition one...

Karl Friedrich Siburg (1993)

Manuscripta mathematica

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Alfred Künzle (1997)

Banach Center Publications

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Symplectic capacities coinciding on convex sets in the standard symplectic vector space are extended to any subsets of symplectic manifolds. It is shown that, using embeddings of non-smooth convex sets and a product formula, calculations of some capacities become very simple. Moreover, it is proved that there exist such capacities which are distinct and that there are star-shaped domains diffeomorphic to the ball but not symplectomorphic to any convex set.