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

Abstract

Basic aspects of the equiaffine geometry of level sets are developed systematically. As an application there are constructed families of $2n$-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.

Corrected multiple typos in displayed equation (2.22) in Remark 2.7 (Remark 2.13 in the published version) and a sign error in the final line of the second paragraph of Example 2.9 (Example 2.17 in the published version). Neither correction is consequential, but the errors in the formulas could have made comparison with other sources confusing

References in corpus (2)

• Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian
• A Schwarz lemma for Kähler affine metrics and the canonical potential of a proper convex cone