On centroaffine Tchebychev hypersurfaces with constant sectional curvature

DOI10.1007/s00025-022-01715-3zbMath1503.53021OpenAlexW4285390475MaRDI QIDQ2159707

Xiuxiu Cheng, Cheng Xing, Ze-Jun Hu

Publication date: 2 August 2022

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-022-01715-3

zbMATH Keywords

constant sectional curvatureTchebychev vector fieldcentroaffine hypersurfaceTchebychev hypersurface

Mathematics Subject Classification ID

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

Related Items (3)

On flat elliptic centroaffine Tchebychev hypersurfaces ⋮ Centroaffine \(T\)-umbilical hypersurfaces and pseudo-parallel cubic form ⋮ On conformally flat centroaffine hypersurfaces with semi-parallel cubic form

Cites Work

• Unnamed Item
• Unnamed Item
• Rigidity theorems for relative Tchebychev hypersurfaces
• Locally strongly convex affine hypersurfaces with parallel cubic form
• On product affine hyperspheres in \(\mathbb{R}^{n+1}\)
• Complete hyperbolic Tchebychev hypersurfaces
• Relative Tchebychev hypersurfaces which are also translation hypersurfaces
• Uniqueness theorems in affine differential geometry. II
• Canonical centroaffine hypersurfaces in \({\mathbb{R}{}}^{n+1}\)
• Centroaffine minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
• Conformal structure in affine geometry: Complete Tchebychev hypersurfaces
• Cubic form methods and relative Tchebychev hypersurfaces
• The Magid-Ryan conjecture for equiaffine hyperspheres with constant sectional curvature.
• On the isolation phenomena of locally conformally flat manifolds with constant scalar curvature -- submanifolds versions
• Centroaffine Bernstein problems
• The centroaffine Tchebychev operator
• Flat hyperbolic Centro-affine Tchebychev hypersurfaces of \(\mathbb{R}^4\)
• Every centroaffine Tchebychev hyperovaloid is ellipsoid
• Classification of the locally strongly convex centroaffine hypersurfaces with parallel cubic form
• Affine spheres with constant affine sectional curvature
• RELATIVE TCHEBYCHEV SURFACES IN R3
• A new centroaffine characterization of the ellipsoids
• A rigidity theorem for centroaffine Chebyshev hyperovaloids
• Global affine differential geometry of hypersurfaces

This page was built for publication: On centroaffine Tchebychev hypersurfaces with constant sectional curvature