\(\delta\)-invariants and their applications to centroaffine geometry

DOI10.1016/J.DIFGEO.2005.01.008zbMath1075.53012OpenAlexW2143591931WikidataQ115357978 ScholiaQ115357978MaRDI QIDQ558086

Leopold Verstraelen, Bang-Yen Chen, Frankie Dillen

Publication date: 30 June 2005

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2005.01.008

zbMATH Keywords

Inequality\(\delta\)-invariantsAffine hypersphereCentroaffine hypersurfaceChebyshev vector fieldClassification theorem

Mathematics Subject Classification ID

Global submanifolds (53C40) Local submanifolds (53B25) Local Riemannian geometry (53B20) Affine differential geometry (53A15)

Related Items (11)

Recent developments in δ-Casorati curvature invariants ⋮ Inequalities for Algebraic Casorati Curvatures and Their Applications II ⋮ Isotropic affine hypersurfaces of dimension 5 ⋮ Locally strongly convex affine hyperspheres realizing Chen's equality ⋮ An optimal inequality and extremal classes of affine spheres in centroaffine geometry ⋮ Improved Chen-Ricci inequality for curvature-like tensors and its applications ⋮ Riemannian submersions with minimal fibers and affine hypersurfaces ⋮ On the sectional curvature of lightlike submanifolds ⋮ On Chen ideal submanifolds satisfying some conditions of pseudo-symmetry type ⋮ On locally strongly convex affine hyperspheres realizing Chen's equality ⋮ Geometry of affine warped product hyperspaces

Cites Work

• Some relations between Riemannian and affine geometry
• Some pinching and classification theorems for minimal submanifolds
• An extremal class of three-dimensional hyperbolic affine spheres
• Canonical centroaffine hypersurfaces in \({\mathbb{R}{}}^{n+1}\)
• The fundamental theorems of curves and hypersurfaces in centro-affine geometry
• Centroaffine minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
• Calabi-type composition of affine spheres
• A new intrinsic curvature invariant for centroaffine hypersurfaces
• Cubic form geometry for immersions in centro-affine and graph hypersurfaces
• The Magid-Ryan conjecture for equiaffine hyperspheres with constant sectional curvature.
• An optimal inequality and extremal classes of affine spheres in centroaffine geometry
• Ideal Lagrangian immersions in complex space forms
• Global affine differential geometry of hypersurfaces
• An extremal class of 3-dimensional elliptic affine spheres
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