A classification of isotropic affine hyperspheres
A classification of isotropic affine hyperspheres
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DOI：
10.1142/s0129167x16500749
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发表时间：
2016-09
影响因子：
0.6
通讯作者：
Marilena Moruz;L. Vrancken
中科院分区：
文献类型：
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作者：
Marilena Moruz;L. Vrancken
我们研究具有各向同性差张量的仿射超曲面 M。请注意，任何表面总是具有各向同性差分张量。如果度量是正定的，则此类超曲面先前已在 [O. Birembaux 和 M. Djoric，各向同性仿射球，数学学报。 Sinica 28(10) 1955–1972.] 和 [O. Birembaux 和 L. Vrancken，5 维各向同性仿射超曲面，J. Math。肛门。应用。 417(2) (2014) 918–962.] 我们首先证明各向同性仿射超曲面的维数是 5、8、14 或 26。接下来，我们假设 M 是仿射超球面，并且我们为每个可能的维度获得完整的分类。
We study affine hypersurfaces M, 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 5, 8, 14 or 26. Next, we assume that M is an affine hypersphere and we obtain for each of the possible dimensions a complete classification.