Geodesic
On the Geometry of Lagrangian Submanifolds
Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 36-51

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We prove that a Lagrangian submanifold passes through each point of a symplectic manifold in the direction of arbitrary Lagrangian plane at this point. Generally speaking, such a Lagrangian submanifold is not unique; nevertheless, the set of all such submanifolds in Hermitian extension of a symplectic manifold of dimension greater than 4 for arbitrary initial data contains a totally geodesic submanifold (which we call the $s$-Lagrangian submanifold) if this symplectic manifold is a complex space form. We show that each Lagrangian submanifold in a complex space form of holomorphic sectional curvature equal to $c$ is a space of constant curvature $c/4$. We apply these results to the geometry of principal toroidal bundles. 
@article{MZM_2001_69_1_a3,
     author = {V. F. Kirichenko},
     title = {On the {Geometry} of {Lagrangian} {Submanifolds}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {36--51},
     publisher = {mathdoc},
     volume = {69},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a3/}
}
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V. F. Kirichenko. On the Geometry of Lagrangian Submanifolds. Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 36-51. http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a3/