arXiv subjects

Michal Szancer

Publications and source records attributed to Michal Szancer.

2 recordsLinked to original sources

arXiv2021

Affine hypersurfaces of arbitrary signature with an almost symplectic form

In this paper we study affine hypersurfaces with non-degenerate second fundamental form of arbitrary signature additionally equipped with an almost symplectic structure $ω$. We prove that if $R^pω=0$ or $\nabla^pω=0$ for some positive integer $p$ then the rank of the shape operator is at most one. The results provide complete classification of affine hypersurfaces with higher order parallel almost symplectic forms and are generalization of recently obtained results for Lorentzian affine hypersurfaces.

math.DG↗

arXiv2018

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

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 $R^k\cdot ω=0$ or $\nabla^kω=0$ 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.

math.DG↗