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Affine Isometric Embedding for Surfaces |
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| Authors: | Thomas Ivey |
| Affiliation: | (1) Department of Mathematics, Case Western Reserve University, 10900, Euclid Avenue, Cleveland, Ohio, 44106-7058, U.S.A;(2) Present address: Department of Mathematical Sciences, Ball State University, Muncie, IN, 47306, U.S.A. |
| 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. |
| Keywords: | affine differential geometry isometric embedding. |
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