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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


The Gauss map for surfaces. I. The affine case

Author: Joel L. Weiner
Journal: Trans. Amer. Math. Soc. 293 (1986), 431-446
MSC: Primary 53A07; Secondary 53A05
MathSciNet review: 816302
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Abstract: Let $ M$ be a connected oriented surface and let $ G_2^c$ be the Grassmannian of oriented $ 2$-planes in Euclidean $ (2 + c)$-space, $ {{\mathbf{E}}^{2 + c}}$. Smooth maps $ t:M \to G_2^c$ are studied to determine whether or not they are Gauss maps. Both local and global results are obtained. If $ t$ is a Gauss map of an immersion $ X:\;M \to {{\mathbf{E}}^{2 + c}}$, we study the extent to which $ t$ uniquely determines $ X$ under certain circumstances.

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PII: S 0002-9947(1986)0816302-8
Keywords: Orientable surface, Gauss map of an immersion, Grassmannian
Article copyright: © Copyright 1986 American Mathematical Society