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Mat. Zametki, 2001, Volume 69, Issue 1, Pages 36–51 (Mi mz482)  

On the Geometry of Lagrangian Submanifolds

V. F. Kirichenko

Moscow State Pedagogical University

Abstract: 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.

DOI: https://doi.org/10.4213/mzm482

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English version:
Mathematical Notes, 2001, 69:1, 32–45

Bibliographic databases:

UDC: 514.76
Received: 16.03.1999
Revised: 22.05.2000

Citation: V. F. Kirichenko, “On the Geometry of Lagrangian Submanifolds”, Mat. Zametki, 69:1 (2001), 36–51; Math. Notes, 69:1 (2001), 32–45

Citation in format AMSBIB
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