An optimal inequality on locally strongly convex centroaffine hypersurfaces

DOI10.1007/s12220-017-9836-xzbMath1392.53017arXiv1702.01534OpenAlexW2592877081MaRDI QIDQ1742960

Xiuxiu Cheng, Ze-Jun Hu

Publication date: 12 April 2018

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.01534

zbMATH Keywords

Tchebychev vector fielddifference tensorlocally strongly convexcentroaffine hypersurfaceparallel cubic form

Mathematics Subject Classification ID

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

Related Items (12)

On product affine hyperspheres in \(\mathbb{R}^{n+1}\) ⋮ Minimal Legendrian submanifolds of $\mathbb S^{9}$ with nonnegative sectional curvature ⋮ An optimal inequality related to characterizations of the contact Whitney spheres in Sasakian space forms ⋮ Classification of locally strongly convex isotropic centroaffine hypersurfaces ⋮ \(\delta^{\sharp}(2,2)\)-ideal centroaffine hypersurfaces of dimension 4 ⋮ Centroaffine \(T\)-umbilical hypersurfaces and pseudo-parallel cubic form ⋮ On conformally flat centroaffine hypersurfaces with semi-parallel cubic form ⋮ Classification of Calabi hypersurfaces with parallel Fubini-Pick form ⋮ Unnamed Item ⋮ A rigidity theorem for centroaffine Chebyshev hyperovaloids ⋮ Every centroaffine Tchebychev hyperovaloid is ellipsoid ⋮ A new centroaffine characterization of the ellipsoids

Cites Work

• Unnamed Item
• Unnamed Item
• Completeness of hyperbolic centroaffine hypersurfaces
• Locally strongly convex affine hypersurfaces with parallel cubic form
• On locally strongly convex affine hypersurfaces with parallel cubic form. I
• Isotropic totally real submanifolds
• Canonical centroaffine hypersurfaces in \({\mathbb{R}{}}^{n+1}\)
• Centroaffine surfaces with parallel traceless cubic form
• Centroaffine minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
• Cubic form methods and relative Tchebychev hypersurfaces
• Hypersurfaces with prescribed affine Gauss-Kronecker curvature
• A basic inequality and new characterization of Whitney spheres in a complex space form
• Structure theorems on Riemannian spaces satisfying \(R(X,Y)\cdot R=0\). I: The local version
• Centroaffine Bernstein problems
• The centroaffine Tchebychev operator
• Classification of the locally strongly convex centroaffine hypersurfaces with parallel cubic form
• Classification of locally strongly convex isotropic centroaffine hypersurfaces
• An optimal inequality and extremal classes of affine spheres in centroaffine geometry
• On the isolation phenomena of Einstein manifolds—submanifolds versions
• Global affine differential geometry of hypersurfaces

This page was built for publication: An optimal inequality on locally strongly convex centroaffine hypersurfaces