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 R P 3 \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 2 -manifold arises as an induced structure on an arbitrary nonplanar surface in R P 3 \mathbf {R}{P^3} ; this result should be contrasted to that of Chern (see [6]).
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