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A note on the space of lagrangian submanifolds of a symplectic 4-manifold

✍ Scribed by Tim Swift

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
76 KB
Volume
35
Category
Article
ISSN
0393-0440

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✦ Synopsis

We show that the space of compact lagrangian submanifolds of a symplectic 4-manifold is a coisotropic submanifold of the space of all codimension two submanifolds, the latter being equipped with a natural symplectic structure. The characteristic foliation of this coisotropic submanifold is shown to coincide with the isodrastic foliation of Weinstein. We also show that the space of lagrangian submanifolds diffeomorphic to the 2-sphere is a lagrangian submanifold.

πŸ“œ SIMILAR VOLUMES

A note on the boundary of a static Loren
A note on the boundary of a static Lorentzian manifold
✍ Rossella Bartolo; Anna Germinario; Miguel SΓ‘nchez πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 99 KB

In this paper we characterize the convexity of the boundary βˆ‚S of a static (standard) Lorentzian manifold S in terms of Jacobi metrics. From this result, we also obtain: (1) a characterization of the convexity of βˆ‚S computable from its "spacelike" part, (2) the equivalence between the variational an