Equivalence problems in projective differential geometry

Yang, Kichoon

doi:10.1090/S0002-9947-1984-0728715-1

Equivalence problems in projective differential geometry
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by Kichoon Yang

Trans. Amer. Math. Soc. 282 (1984), 319-334

DOI: https://doi.org/10.1090/S0002-9947-1984-0728715-1

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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]).

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