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arXiv · 1404.2609

Affine metrics of locally strictly convex surfaces in affine 4-space

Juan J. Nuño Ballesteros·Luis Sánchez
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Abstract

We introduce a new family of affine metrics on a locally strictly convex surface $M$ in affine 4-space. Then, we define the symmetric and antisymmetric equiaffine planes associated with each metric. We show that if $M$ is immersed in a locally strictly convex hyperquadric, then the symmetric and the antisymmetric planes coincide and contain the affine normal to the hyperquadric. In particular, any surface immersed in a locally strictly convex hyperquadric is affine semiumbilical with respect to the symmetric or antisymmetric equiaffine planes.

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Juan J. Nuño Ballesteros, Luis Sánchez. 2014-04-09. Affine metrics of locally strictly convex surfaces in affine 4-space. https://arxiv.org/abs/1404.2609

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