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arXiv · 2211.02814

Conformally flat affine hypersurfaces with semi-parallel cubic form

Huiyang Xu·Cece Li
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Abstract

In this paper, we study locally strongly convex affine hypersurfaces with vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of affine metric. As the main result, we classify such hypersurfaces being not of flat affine metric. In particular, $2, 3$-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic form are completely determined.

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Huiyang Xu, Cece Li. 2022-11-05. Conformally flat affine hypersurfaces with semi-parallel cubic form. https://doi.org/10.1007/s10473-023-0606-5

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