On normal and conormal maps for affine hypersurfaces

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概要

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• We prove two main results in affine differential geometry that characterize ellipsoids among the ovaloids. The first theorem states that an ovaloid in the 3-dimensional affine space is an ellipsoid if and only if the Laplacian of the normal map is proportional to the normal map. The second theorem says that a hyperovaloid in an affine space of any dimension is a hyperellipsoid if and only if the conormal image (or the normal image) is a hyperellipsoid with center at the origin.

• 東北大学の論文

著者

• NOMIZU Katsumi

  Department of Mathematics Brown University

• Opozda Barbara

  Instytut Matematyki UJ,

• Opozda Barbara

  Instytut Matematyki Uj

関連論文

• On the geometry of projective immersions
• On the geometry of affine Kahler immersions
• On the Cartan-Norden theorem for affine Kahler immersions
• On affine hypersurfaces with parallel nullity
• Globally defined linear connections on the real line and the circle
• Affine hypersurfaces with parallel cubic forms
• On certain quartic forms for affine surfaces
• On normal and conormal maps for affine hypersurfaces
• Cayley surfaces in affine differential geometry
• Weak geometric structures on submanifolds of affine spaces
• SURFACES WHOSE AFFINE NORMAL IMAGES ARE CURVES

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