Uniqueness theorems in affine differential geometry. II

DOI10.1007/BF03323247zbMath0646.53009WikidataQ115390772 ScholiaQ115390772MaRDI QIDQ1103881

Gabi Penn, An-Min Li

Publication date: 1988

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

zbMATH Keywords

convex surfacescomplete equiaffine surfacesequiaffine scalar curvature

Mathematics Subject Classification ID

Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Affine differential geometry (53A15)

Related Items (25)

On product affine hyperspheres in \(\mathbb{R}^{n+1}\) ⋮ On locally symmetric affine hypersurfaces ⋮ Calabi-type composition of affine spheres ⋮ Affine spheres with constant affine sectional curvature ⋮ Some theorems in affine differential geometry ⋮ On Lorentzian Einstein affine hyperspheres ⋮ On centroaffine Tchebychev hypersurfaces with constant sectional curvature ⋮ On flat elliptic centroaffine Tchebychev hypersurfaces ⋮ Minimal Legendrian submanifolds in Sasakian space forms with \(C\)-parallel second fundamental form ⋮ On affine surfaces whose cubic forms are parallel relative to the affine metric ⋮ The Magid-Ryan conjecture for \(4\)-dimensional affine spheres ⋮ Asymptotics of Laplacians defined by symmetric connections ⋮ On the Pick invariant, the affine mean curvature and the Gauss curvature of affine surfaces ⋮ Canonical centroaffine hypersurfaces in \({\mathbb{R}{}}^{n+1}\) ⋮ Affine quasi umbilical hypersurfaces which are flat with respect to the affine metric ⋮ Classification of Calabi hypersurfaces with parallel Fubini-Pick form ⋮ Pick invariant and affine Gauss-Kronecker curvature ⋮ Lorentzian affine hyperspheres with constant affine sectional curvature ⋮ Affine surfaces with higher order parallel cubic form ⋮ Unnamed Item ⋮ On four-dimensional Einstein affine hyperspheres ⋮ An affine invariant characterization of flat gravity curves ⋮ Improper affine spheres in \(\mathbb{R}^ 3\) and \(\mathbb{C}^ 3\) ⋮ Local classification of twodimensional affine spheres with constant curvature metric ⋮ Canonical equiaffine hypersurfaces in \(\mathbb{R}^{n+1}\)

Cites Work

• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens

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