## On stability of constrained Lagrangian submanifolds.(English)Zbl 0546.58023

The notion of stability of constrained Lagrangian submanifolds of symplectic manifold, with respect to the two special symplectic structures, is introduced. In the case of dimension 5 of a Lagrangian submanifold and dimension 2 of the constraint, the classification and description of the stable constrained Lagrangian submanifolds are given. The author starts with the basic definitions and theorems, then the classification problem for stable Lagrangian submanifolds is formulated. Next, the main theorem of the paper stating the normal forms of stable constrained Lagrangian submanifolds of constraint dimension less than or equal to two is proved. An example of an application of the presented approach is also given.
Reviewer: W.Waliszewski

### MSC:

 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 53C80 Applications of global differential geometry to the sciences