منابع مشابه
Projective embedding of projective spaces
In this paper, embeddings φ : M → P from a linear space (M,M) in a projective space (P,L) are studied. We give examples for dimM > dimP and show under which conditions equality holds. More precisely, we introduce properties (G) (for a line L ∈ L and for a plane E ⊂ M it holds that |L ∩ φ(M)| 6 = 1) and (E) (φ(E) = φ(E) ∩ φ(M), whereby φ(E) denotes the by φ(E) generated subspace of P ). If (G) a...
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1. Haefliger reduced the question of embedding manifolds in the Euclidian space R to a homotopy problem in [ö]. Since then it has been of some interest to find examples of ^-manifolds which embed in R~ for a given k. In particular great effort has been spent studying embeddings of the various projective spaces. However, the k that were thus obtained were in no cases larger than 5 or 6 (see for ...
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We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our concepts to the problem of describing dual spreads. We do not assume that the projective space is finitedimensional or pappian. Mathematics Subject Classification...
متن کاملMetrizations of Projective Spaces
A two-dimensional G-space,1 in which the geodesic through two distinct points is unique, is either homeomorphic to the plane £2 and all geodesies are isometric to a straight line, or it is homeomorphic to the projective plane P2 and all geodesies are isometric to the same circle, see [l, §§10 and 31 ]. Two problems arise in either case: (1) To determine the systems of curves (in E2 or P2) which...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1970
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1970-0280501-0