Projectively flat affine surfaces that are not locally symmetric
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 by Isaac Chaujun Lee PDF
 Proc. Amer. Math. Soc. 123 (1995), 237246 Request permission
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.References

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Additional Information
 © Copyright 1995 American Mathematical Society
 Journal: Proc. Amer. Math. Soc. 123 (1995), 237246
 MSC: Primary 53A15; Secondary 53C05, 53C40
 DOI: https://doi.org/10.1090/S00029939199512122850
 MathSciNet review: 1212285