Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Affine $ 3$-spheres with constant affine curvature

Authors: Martin A. Magid and Patrick J. Ryan
Journal: Trans. Amer. Math. Soc. 330 (1992), 887-901
MSC: Primary 53C40; Secondary 53A15
MathSciNet review: 1062193
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Abstract: We classify the affine hyperspheres in $ {R^4}$ which have constant curvature in the affine metric $ h$ and whose Pick invariant is nonzero. In particular, the metric $ h$ must be flat.

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Keywords: Affine sphere, Pick invariant
Article copyright: © Copyright 1992 American Mathematical Society