Affine hypersurfaces with constant sectional curvature

DOI10.2140/pjm.2021.310.275zbMath1467.53010OpenAlexW3135179671MaRDI QIDQ2658489

Haizhong Li, Luc Vrancken, Xian Feng Wang, Miroslava Antić

Publication date: 23 March 2021

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.2021.310.275

zbMATH Keywords

affine hypersurfaceconstant sectional curvatureaffine hypersphereaffine metric

Mathematics Subject Classification ID

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

Related Items (13)

Non-existence of conformally flat real hypersurfaces in both the complex quadric and the complex hyperbolic quadric ⋮ Conformally flat affine hypersurfaces with semi-parallel cubic form ⋮ Locally strongly convex affine hypersurfaces with semi-parallel cubic form ⋮ Cyclic semi-parallel real hypersurfaces in complex Grassmannians of rank two ⋮ Multiple product affine hypersurfaces with semi-parallel cubic form ⋮ Locally conformally flat affine hyperspheres with parallel Ricci tensor ⋮ Classification of semi-parallel hypersurfaces of the product of two spheres ⋮ On conformally flat affine hypersurfaces with pseudo-parallel cubic form ⋮ Warped product hypersurfaces in pseudo-Riemannian real space forms ⋮ On locally strongly convex affine hyperspheres realizing Chen's equality ⋮ Lagrangian warped product immersions in \(\mathbb{S}^6\) ⋮ New equiaffine characterizations of the ellipsoids related to an equiaffine integral inequality on hyperovaloids ⋮ On \(C\)-totally real minimal submanifolds of the Sasakian space forms with parallel Ricci tensor

Cites Work

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• On locally strongly convex affine hypersurfaces with parallel cubic form. I
• The Magid-Ryan conjecture for equiaffine hyperspheres with constant sectional curvature.
• Affine spheres with constant affine sectional curvature
• Complete affine hypersurfaces. Part I. The completeness of affine metrics
• Affine 3-Spheres with Constant Affine Curvature
• DECOMPOSABLE AFFINE HYPERSURFACES
• Global affine differential geometry of hypersurfaces

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