Affine manifolds, lagrangian manifolds

Details Affine manifolds, lagrangian manifolds Affine manifolds, lagrangian manifolds

2003-08-22

arxiv.org/abs/math/0308217v1

Mathematics

Differential Geometry

14 pages 16 references

Scientific paper

Let $(M,\omega)$ be a symplectic manifold endowed with a agrangian foliation ${\cal L}$, it has been shown by Weinstein [16] hat the symplectic structure of $M$ defines on each leaf of ${\cal L}$, connection which curvature and torsion forms vanish identically. uppose that $L_0$ is a compact leaf which Weinstein connection is eodesically complete, Molino and Curras-Bosch [2] have classified erms of such lagrangian foliation around $L_0$. In this paper we xtend this classification without supposing the completness of he compact leaf. The Weinstein connection is dual to the Bott onnection, this enables to relate the conjecture of Auslander nd Markus to transversally properties of these foliations.

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