On the cycle of singularities of isotropic submanifolds (Q1267464)

The authors prove the following Theorem. If \(L\subset \mathbb{R}^{2n}\) is an \(r\)-dimensional isotropic submanifold, \(r<n\), then by an orthogonal symplectic linear transformation arbitrarily close to the identity transformation one can bring \(L\) to a position such that the following condition is satisfied: all the \(\Gamma^i\) are smooth manifolds of codimension \[ \text{codim} \Gamma^i={i(i+1)\over 2}+id,\quad i=1,2,\dots \] where \(d=n-r\) is the dimension deficiency of \(L\) and \(\Gamma(L)\) is the cycle of singularities of \(L:\Gamma(L)= \bigcup_{i\geq 1}\Gamma^i\), where \(\Gamma^i=\Gamma^i(L)= \{\alpha\in L\mid\) the rank of the projection \(P\): \(L\to\mathbb{R}^n_x\) at \(\alpha\) is \(r-i\}\).