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arXiv · 1702.01534

An optimal inequality on locally strongly convex centroaffine hypersurfaces

Xiuxiu Cheng·Zejun Hu
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Abstract

In this paper, we establish a general inequality for locally strongly convex centroaffine hypersurfaces in $\mathbb{R}^{n+1}$ involving the norm of the covariant derivatives of both the difference tensor $K$ and the Tchebychev vector field $T$. Our result is optimal in that, applying our recent classification for locally strongly convex centroaffine hypersurfaces with parallel cubic form in [4], we can completely classify the hypersurfaces which realize the equality case of the inequality.

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Xiuxiu Cheng, Zejun Hu. 2017-02-06. An optimal inequality on locally strongly convex centroaffine hypersurfaces. https://doi.org/10.1007/s12220-017-9836-x

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