Abstract
We study affine hypersurfaces [Formula: see text], which have isotropic difference tensor. Note that, any surface always has isotropic difference tensor. In case that the metric is positive definite, such hypersurfaces have been previously studied in [O. Birembaux and M. Djoric, Isotropic affine spheres, Acta Math. Sinica 28(10) 1955–1972.] and [O. Birembaux and L. Vrancken, Isotropic affine hypersurfaces of dimension 5, J. Math. Anal. Appl. 417(2) (2014) 918–962.] We first show that the dimension of an isotropic affine hypersurface is either [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text]. Next, we assume that [Formula: see text] is an affine hypersphere and we obtain for each of the possible dimensions a complete classification.
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