Immersions and Embeddings of Projective Spaces
نویسندگان
چکیده
منابع مشابه
CR Singular Immersions of Complex Projective Spaces
Quadratically parametrized smooth maps from one complex projective space to another are constructed as projections of the Segre map of the complexification. A classification theorem relates equivalence classes of projections to congruence classes of matrix pencils. Maps from the 2-sphere to the complex projective plane, which generalize stereographic projection, and immersions of the complex pr...
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The question of finding the smallest Euclidean space in which real projective space P n can be (differentiably) embedded was the subject of intense investigation during the 1960s and 1970s. The purpose of this paper is to survey the status of the question, and add a little bit to our knowledge by proving one new family of embeddings, using old methods of obstruction theory. Our new result is gi...
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In every differential topology textbook one finds Whitney’s immersion and embedding theorems. But, the real story of immersions started with the results of Hirsch ([15]) and Smale ([30]). We do not intend to follow closely all these developments. Rather, we restrict ourselves mainly to the problem of the existence of immersions of real projective spaces into Euclidean spaces and the problems re...
متن کاملGeneralized Veronesean embeddings of projective spaces
We classify all embeddings θ : PG(n, q) −→ PG(d, q), with d ≥ n(n+3) 2 , such that θ maps the set of points of each line to a set of coplanar points and such that the image of θ generates PG(d, q). It turns out that d = 1 2n(n+3) and all examples are related to the quadric Veronesean of PG(n, q) in PG(d, q) and its projections from subspaces of PG(d, q) generated by sub-Veroneseans (the point s...
متن کاملGeneralized lax Veronesean embeddings of projective spaces
We classify all embeddings θ : PG(n,K) −→ PG(d,F), with d ≥ n(n+3) 2 and K,F skew fields with |K| > 2, such that θ maps the set of points of each line of PG(n,K) to a set of coplanar points of PG(d,F), and such that the image of θ generates PG(d,F). It turns out that d = 12n(n+ 3) and all examples “essentially” arise from a similar “full” embedding θ′ : PG(n,K) −→ PG(d,K) by identifying K with ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1972
ISSN: 0002-9939
DOI: 10.2307/2037654