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

Michal Szancer and Zuzanna Szancer

Mathematische Nachrichten, 2020, vol. 293, issue 8, 1613-1628

Abstract: In 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 Rk·ω=0 or ∇kω=0 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.

Date: 2020
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https://doi.org/10.1002/mana.201900269

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