A new centroaffine characterization of the ellipsoids

DOI10.1090/proc/15504zbMath1469.53017OpenAlexW3131363952MaRDI QIDQ4992935

Cheng Xing, Ze-Jun Hu

Publication date: 10 June 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/15504

zbMATH Keywords

ellipsoidintegral inequalitycentroaffine hypersurfaceChebychev vector fieldhyperovaloid

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Rigidity results (53C24) Affine differential geometry (53A15)

Related Items (5)

On centroaffine Tchebychev hypersurfaces with constant sectional curvature ⋮ Some new characterizations of real hypersurfaces with isometric Reeb flow in complex two-plane Grassmannians ⋮ Centroaffine \(T\)-umbilical hypersurfaces and pseudo-parallel cubic form ⋮ A rigidity theorem for hypersurfaces of the odd-dimensional unit sphere $\mathbb S^{2n+1}(1)$ ⋮ On conformally flat centroaffine hypersurfaces with semi-parallel cubic form

Cites Work

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• An optimal inequality on locally strongly convex centroaffine hypersurfaces
• The centroaffine Tchebychev operator
• Classification of the locally strongly convex centroaffine hypersurfaces with parallel cubic form
• On harmonic and Killing vector fields
• A rigidity theorem for centroaffine Chebyshev hyperovaloids
• Global affine differential geometry of hypersurfaces

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