Projectively flat affine surfaces that are not locally symmetric

Author:
Isaac Chaujun Lee

Journal:
Proc. Amer. Math. Soc. **123** (1995), 237-246

MSC:
Primary 53A15; Secondary 53C05, 53C40

MathSciNet review:
1212285

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Abstract: By studying affine rotation surfaces (ARS), we prove that any surface affine congruent to or is *projectively flat but is neither locally symmetric nor an affine sphere*, where is 1 or , and . The significance of these surfaces is due to the fact that until now 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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DOI:
http://dx.doi.org/10.1090/S0002-9939-1995-1212285-0

Keywords:
Blaschke immersion,
locally symmetric,
projectively flat,
affine rotation surfaces

Article copyright:
© Copyright 1995
American Mathematical Society