Open AccessA new centroaffine characterization of the ellipsoids
Author(s) -
Zejun Hu,
Cheng Xing
Publication year - 2021
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/15504
Subject(s) - ellipsoid , algorithm , curvature , mathematics , artificial intelligence , computer science , geometry , physics , astronomy
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.