Projective deformation of line congruences in five-dimensional projective spaces
نویسندگان
چکیده
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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0.1. Notations and Conventions. During this note, we will fix a base field k (e.g. the complex numbers C). The multiplicative group of the field k will be denoted by Gm. All the vector spaces considered will be finite dimensional vector spaces over the field k. For a given vector space V of dimension≥ 1, we will denote the dual vector space, the projective space parameterizing 1-dimensional sub...
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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: Czechoslovak Mathematical Journal
سال: 1968
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1968.100846