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

作者：Nuno Ballesteros Juan J^*; Sanchez Luis

来源：Geometriae Dedicata, 2016, 183(1): 1-24.

DOI：10.1007/s10711-016-0140-x

• Affine metric
• Affine normal plane
• Affine semiumbilical

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 of 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.

• 出版日期2016-8