3-dimensional affine hypersurfaces admitting a pointwise SO(2)- or Z_3-symmetry

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In (equi-)affine differential geometry, the most important algebraic invariants are the affine (Blaschke) metric h, the affine shape operator S and the difference tensor K. A hypersurface is said to admit a pointwise symmetry if at every point there exists a linear transformation preserving the affine metric, the affine shape operator and the difference tensor K. The study of submanifolds which admit pointwise isometries was initiated by Bryant (math.DG/0007128). In this paper, we consider the 3-dimensional positive definite hypersurfaces for which at each point the group of symmetries is isomorphic to either Z_3 or SO(2). We classify such hypersurfaces and show how they can be constructed starting from 2-dimensional positive definite affine spheres.
22 pages, preprint from Oct. 7, 2002

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Differential Geometry, 53A15

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http://salesiana.dossiersoluciones.com/handle/123456789/66732

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0303099
 http://arxiv.org/abs/math/0303099

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arXiv