Cosymplectic Lagrangian-like Submanifolds in Odd-Dimensional Geometry
The odd-dimensional counterpart of Lagrangian submanifolds, developed inside cosymplectic geometry, where a manifold carries a closed 1-form and closed 2-form whose product is a volume form. Students learn how to define Lagrangian-like subspaces and their Grassmannian in this setting, how compatible co-complex structures behave, and how cosymplectic versions of Moser's trick and the Weinstein neighborhood theorem give local normal forms whose associated 1-form has a de Rham class realized as a co-flux.
2501.00694
This paper builds the theory of 'Lagrangian-like' submanifolds in cosymplectic geometry, the odd-dimensional analogue of symplectic geometry. A cosymplectic structure on a (2n+1)-dimensional manifold…