Abstract
Let $F: \Sigma \to \mathbb{R}^3$ be a Blaschke immersion of an affine surface $(\Sigma,\nabla)$ with a positive definite affine fundamental form such that $dim Im \,\ R = 1$ where $R$ is the curvature tensor. Suppose that there exists another immersion of the same surface with the same induced affine connection $\nabla$ which is not affine equivalent to the first one. Then we give explicitely $F$. Therefore all immersions which admit another immersion which is not affine equivalent to the original one are classified.
Citation
Olivier BIREMBAUX. "Affine surfaces which admit several affine immersions in $\mathbb{R}^3$." Hokkaido Math. J. 38 (2) 205 - 232, May 2009. https://doi.org/10.14492/hokmj/1248190075
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