Abstract
A strictly convex hypersurface in Rn can be endowed with a Riemannian metric in a way that is invariant under the group of (equi)affine motions. We study the corresponding isometric embedding problem for surfaces in R3. This problem is formulated in terms of a quasilinear elliptic system of PDE for the Pick form. A negative result is obtained by attempting to invert about the standard embedding of the round sphere as an ellipsoid.
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Ivey, T. Affine Isometric Embedding for Surfaces. Geometriae Dedicata 75, 235–243 (1999). https://doi.org/10.1023/A:1005091621118
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DOI: https://doi.org/10.1023/A:1005091621118