On 4‐dimensional Lorentzian affine hypersurfaces with an almost symplectic form

Abstract

AbstractIn this paper we study 4‐dimensional affine hypersurfaces with a Lorentzian second fundamental form additionally equipped with an almost symplectic structure ω. We prove that the rank of the shape operator is at most one if or for some positive integer k. This result is the final step in a classification of Lorentzian affine hypersurfaces with higher order parallel almost symplectic forms.