Hokkaido Mathematical Journal

BIREMBAUX Olivier,

Affine surfaces which admit several affine immersions in R^3.

Hokkaido Mathematical Journal, 38 (2009) pp.205-232

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Abstract

Let F:\Sigma\to R^3 be a Blaschke immersion of an affine surface (\Sigma,\Nabla) with a positive definite affine fundamental form such that dim Im R = 1 where R is the curvature tensor. Suppose that there exists another immersion of the same surface with the same induced affine connection \Nabla which is not affine equivalent to the first one. Then we give explicitely F. Therefore all immersions which admit another immersion which is not affine equivalent to the original one are classified.

MSC(Primary)53A15
MSC(Secondary)
Uncontrolled KeywordsBlaschke immersion, affine surface.