Cylinder conjecture for skew branes over non-centrally symmetric hypersurfaces

Let $M^{2n-1}\be2 {\bf R}^{2n}$ be a non-centrally symmetric hypersurface. A skew brane is an $(2n-1)$-dimensional submanifold of ${\bf R}^{2n+1}={\bf R}^{2n}\be2 {\bf R}$; the vertical cylinder over $M$ is $M\be2 {\bf R}$. Cylinder conjecture. For every non-centrally symmetric $M^{2n-1}\be2 {\bf R}^{2n}$ there exists a skew brane $N^{2n-1}\be2 {\bf R}^{2n+1}={\bf R}^{2n}\be2 {\bf R}$ which is a section of the vertical cylinder over $M$. The conjecture asserts existence of such a skew brane for every non-centrally symmetric hypersurface; the source does not provide a resolution.