The Lipschitz-Killing curvature for an equiaffine immersion and theorems of Gauss-Bonnet type and Chern-Lashof type.

DOI10.1007/BF03322688zbMath1033.53010OpenAlexW1991252688MaRDI QIDQ5943572

Naoyuki Koike

Publication date: 21 March 2004

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

Full work available at URL: https://doi.org/10.1007/bf03322688

zbMATH Keywords

affine differential geometryaffine immersions of general codimensiontheorem of Gauss-Bonnet

Mathematics Subject Classification ID

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

Related Items (5)

The total absolute curvature of an equiaffine immersion ⋮ A generalization of Lelieuvre's formula to equiaffine immersions of general codimension ⋮ Theorems of Gauss-Bonnet and Chern-Lashof types in a simply connected symmetric space of non-positive curvature ⋮ Equiaffine immersions of general codimension and its transversal volume element map ⋮ The quadratic slice theorem and the equiaffine tube theorem for equiaffine Dupin hypersurfaces

Cites Work

• On the total curvature of immersed manifolds. II
• Cubic form theorem for affine immersions
• On the Total Curvature of Immersed Manifolds
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