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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中文翻译：

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椭球的新的中心亲和表征

摘要：在本文中，我们根据 Tchebychev 向量场方向的 Ricci 曲率和协变微分的范数，在 $\mathbb {R}^{n+1}$ 中建立了一个关于中心仿射超椭圆形的积分不等式。关于 Centroaffine 度量的 Levi-Civita 连接的差分张量。这种积分不等式是最优的，它的等价情况提供了椭球的新的中心仿射表征。

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