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arXiv · 1812.01089

On $4$-dimensional Lorentzian affine hypersurfaces with an almost symplectic form

Michal Szancer·Zuzanna Szancer
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Abstract

In this paper we study $4$-dimensional affine hypersurfaces with a Lorentzian second fundamental form additionally equipped with an almost symplectic structure $\omega$. We prove that the rank of the shape operator is at most one if $R^k\cdot \omega=0$ or $\nabla^k\omega=0$ 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.

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Michal Szancer, Zuzanna Szancer. 2018-12-03. On $4$-dimensional Lorentzian affine hypersurfaces with an almost symplectic form. https://arxiv.org/abs/1812.01089

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