Centroaffine \(T\)-umbilical hypersurfaces and pseudo-parallel cubic form

DOI10.1007/s00025-023-02045-8OpenAlexW4388794322MaRDI QIDQ6143036

Huiyang Xu, Cece Li

Publication date: 4 January 2024

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

Full work available at URL: https://doi.org/10.1007/s00025-023-02045-8

zbMATH Keywords

warped productsconformally flat metrics\(T\)-umbilical centroaffine hypersurfacespseudo-parallel cubic forms

Mathematics Subject Classification ID

Local submanifolds (53B25) Local Riemannian geometry (53B20) Affine differential geometry (53A15)

Cites Work

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• Lorentzian affine hypersurfaces with parallel cubic form
• Locally strongly convex affine hypersurfaces with parallel cubic form
• Characterization of the generalized Calabi composition of affine hyperspheres
• Centro-affine hypersurface immersions with parallel cubic form
• Complete locally conformally flat manifolds of negative curvature
• Pseudo-parallel Lagrangian submanifolds are semi-parallel
• Canonical centroaffine hypersurfaces in \({\mathbb{R}{}}^{n+1}\)
• Centroaffine surfaces with parallel traceless cubic form
• Centroaffine minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
• Calabi-type composition of affine spheres
• Interaction of Legendre curves and Lagrangian submanifolds
• An optimal inequality on locally strongly convex centroaffine hypersurfaces
• Centroaffine Bernstein problems
• The centroaffine Tchebychev operator
• Isometric immersions of warped products
• Graph immersions with parallel cubic form
• Classification of Calabi hypersurfaces with parallel Fubini-Pick form
• Flat hyperbolic Centro-affine Tchebychev hypersurfaces of \(\mathbb{R}^4\)
• Every centroaffine Tchebychev hyperovaloid is ellipsoid
• On centroaffine Tchebychev hypersurfaces with constant sectional curvature
• On locally strongly convex affine hyperspheres realizing Chen's equality
• Classification of the locally strongly convex centroaffine hypersurfaces with parallel cubic form
• Classification of locally strongly convex isotropic centroaffine hypersurfaces
• Characterizations of the Calabi product of hyperbolic affine hyperspheres
• Affine spheres with constant affine sectional curvature
• Locally strongly convex affine hypersurfaces with semi-parallel cubic form
• On conformally flat centroaffine hypersurfaces with semi-parallel cubic form
• On conformally flat affine hypersurfaces with pseudo-parallel cubic form
• Lagrangian isometric immersions of a real-space-form Mⁿ(c) into a complex-space-form M˜ⁿ(4c)
• A new centroaffine characterization of the ellipsoids
• DECOMPOSABLE AFFINE HYPERSURFACES
• Global affine differential geometry of hypersurfaces

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