Abstract
In this paper we study nondegenerate affine surfaces in the 4-dimensional affine space \(\mathbb{R}^4 \). We assume that both the connection ∇ and the normal connection ∇⊥ induced by the canonical equiaffine transversal bundle are flat. Surfaces with constant equiaffine transversal bundle are trivial examples of such surfaces. Here, we obtain a complete classification of all such surfaces which do not have constant equiaffine normal bundle.
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Magid, M., Vrancken, L. Flat Affine Surfaces in \(\mathbb{R}^4 \) with Flat Normal Connection. Geometriae Dedicata 81, 19–31 (2000). https://doi.org/10.1023/A:1005267821555
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DOI: https://doi.org/10.1023/A:1005267821555