Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Projectively flat affine surfaces that are not locally symmetric
HTML articles powered by AMS MathViewer

by Isaac Chaujun Lee PDF
Proc. Amer. Math. Soc. 123 (1995), 237-246 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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53A15, 53C05, 53C40
  • Retrieve articles in all journals with MSC: 53A15, 53C05, 53C40
Additional 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