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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Equivalence problems in projective differential geometry
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by Kichoon Yang PDF
Trans. Amer. Math. Soc. 282 (1984), 319-334 Request permission

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
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • 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