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Basic aspects of the equiaffine geometry of level sets are developed systematically. As an application there are constructed families of 2 n ‐dimensional nondegenerate hypersurfaces ruled by  n ‐planes, having equiaffine mean curvature zero, and solving the affine normal flow. Each carries a symplectic structure with respect to which the ruling is Lagrangian.

Equiaffine geometry of level sets and ruled hypersurfaces with equiaffine mean curvature zero