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Flat affine spheres in R 3

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Abstract

Nondegenerate affine surfaces in R 3 which are affine spheres and have flat affine metrics are classified. Those spheres which are proper are shown to be equivalent to open subsets of the surface defined by xyz=1 or the surface defined by (x 2+y 2)z=1.

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Partially supported by NSF Grant DMS 8802664.

Partially supported by NSERC Operating Grant A2501.

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Magid, M.A., Ryan, P.J. Flat affine spheres in R 3 . Geom Dedicata 33, 277–288 (1990). https://doi.org/10.1007/BF00181334

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  • DOI: https://doi.org/10.1007/BF00181334

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