In this paper the germ of neighborhood of a compact leaf in a Lagrangian foliation is symplectically classified when the compact leaf is $\bT^2$, the affine structure induced by the Lagrangian foliation on the leaf is complete, and the holonomy of $\bT^2$ in the foliation linearizes. The germ of neighborhood is classified by a function, depending on one transverse coordinate, this function is related to the affine structure of the nearly compact leaves.

Keywords:

symplectic manifold, Lagrangian foliation, affine connection symplectic manifold, Lagrangian foliation, affine connection

MSC Classifications:

53C12, 58F05 show english descriptions Foliations (differential geometric aspects) [See also 57R30, 57R32]
unknown classification 58F05 53C12 - Foliations (differential geometric aspects) [See also 57R30, 57R32]
58F05 - unknown classification 58F05

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