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Transactions of the American Mathematical Society

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Equivalence problems in projective differential geometry


Author: Kichoon Yang
Journal: Trans. Amer. Math. Soc. 282 (1984), 319-334
MSC: Primary 53B10; Secondary 53B25
DOI: https://doi.org/10.1090/S0002-9947-1984-0728715-1
MathSciNet review: 728715
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Abstract: Equivalence problems for abstract, and induced, projective structures are investigated. (i) The notion of induced projective structures on submanifolds of a projective space is rigorously defined. (ii) Equivalence problems for such structures are discussed; in particular, it is shown that nonplanar surfaces in $ \mathbf{R}{P^3}$ are all projectively equivalent to each other. (iii) The imbedding problem of abstract projective structures is studied; in particular, we show that every abstract projective structure on a $ 2$-manifold arises as an induced structure on an arbitrary nonplanar surface in $ \mathbf{R}{P^3}$; this result should be contrasted to that of Chern (see [6]).


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9947-1984-0728715-1
Article copyright: © Copyright 1984 American Mathematical Society