A new centroaffine characterization of the ellipsoids

Hu, Zejun; Xing, Cheng

doi:10.1090/proc/15504

A new centroaffine characterization of the ellipsoids
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by Zejun Hu and Cheng Xing

Proc. Amer. Math. Soc. 149 (2021), 3531-3540

DOI: https://doi.org/10.1090/proc/15504

Published electronically: May 10, 2021

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Abstract:

In this paper, we establish an integral inequality on centroaffine hyperovaloids in $\mathbb {R}^{n+1}$, in terms of the Ricci curvature in direction of the Tchebychev vector field and the norm of the covariant differentiation of the difference tensor with respect to the Levi-Civita connection of the centroaffine metric. This integral inequality is optimal, and its equality case provides a new centroaffine characterization of the ellipsoids.

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