Flat Affine Surfaces in mathbb{R}^4 with Flat Normal Connection |
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| Authors: | Martin Magid Luc Vrancken |
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| Affiliation: | (1) Department of Mathematics, Wellesley College, Wellesley, MA, 02181, U.S.A.;(2) Fachbereich Mathematik, T.U. Berlin, Sekr. MA8–3, Strasse des 17 Juni 136, 110623 Berlin, Germany |
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| Abstract: | In this paper we study nondegenerate affine surfaces in the 4-dimensional affine space  . 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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| Keywords: | Codazzi equation torsion-free connection equiaffine normal plane |
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