Lagrangian submanifolds satisfying Maslov's quantization condition
In this talk I will explain the so-called Maslov quantization condition and related examples.
Starting from Bohr's hydrogen model, a classical and famous condition, the Maslov quantization condition, has been of interest since it guarantees the existence of a certain sequence of eigenvalues of the Laplacian.
After some introduction I explain an operator theoretical meaning of the role deduced by the existence of Lagrangian submanifolds. It is formulated as "Eigenvalue Theorem". Particularly, I will explain its meaning from the view point of Fourier integral operator theory.
The main content of this talk is to show the existence of such a Lagrangian submanifold on a particular manifold, namely the Cayley projective plane. The construction is explicitly based on the realization of the punctured cotangent bundle of the Cayley projective plane in the complex space C27 \{0}.
If there is time, I will explain a behavior of Lagrangian submanifolds under submersion and a related example.
