## Projectively flat affine surfaces that are not locally symmetric

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- by Isaac Chaujun Lee
- Proc. Amer. Math. Soc.
**123**(1995), 237-246 - DOI: https://doi.org/10.1090/S0002-9939-1995-1212285-0
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## Abstract:

By studying affine rotation surfaces (ARS), we prove that any surface affine congruent to ${x^2} + \epsilon {y^2} = {z^r}$ or ${y^2} = z(x + \epsilon z\log z)$ is*projectively flat but is neither locally symmetric nor an affine sphere*, where $\epsilon$ is 1 or $- 1, r \in {\mathbf {R}} - \{ - 1,0,1,2\}$, and $z > 0$. The significance of these surfaces is due to the fact that until now ${x^2} + \epsilon {y^2} = {z^{ - 1}}$ are the only known surfaces which are projectively flat but not locally symmetric. Although Podestà recently proved the existence of an affine surface satisfying the above italicized conditions, he did not construct any concrete example.

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## Bibliographic Information

- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**123**(1995), 237-246 - MSC: Primary 53A15; Secondary 53C05, 53C40
- DOI: https://doi.org/10.1090/S0002-9939-1995-1212285-0
- MathSciNet review: 1212285