A new centroaffine characterization of the ellipsoids-Reference-Cited by-同舟云学术

A new centroaffine characterization of the ellipsoids

Published:2021-05-10 Issue:8 Volume:149 Page:3531-3540
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Hu Zejun,Xing Cheng

Abstract

In this paper, we establish an integral inequality on centroaffine hyperovaloids in R n + 1 \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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/proc/earlyview/#proc15504/.pdf

Reference14 articles.

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2. Classification of the locally strongly convex centroaffine hypersurfaces with parallel cubic form;Cheng, Xiuxiu;Results Math.,2017

3. Xiuxiu Cheng, Zejun Hu, and Luc Vrancken, Every centroaffine Tchebychev hyperovaloid is ellipsoid, arXiv:1911.05222.

4. A rigidity theorem for centroaffine Chebyshev hyperovaloids;Cheng, Xiuxiu;Colloq. Math.,2019

5. Rigidity theorems for relative Tchebychev hypersurfaces;Li, Ming;Results Math.,2016

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