منابع مشابه
Polar spaces embedded in projective spaces
Let P be a polar space induced by a quasipolarity on a projective space G. In this article, we give sufficient conditions for an embedding (i.e. an incidence-preserving map which is injective on points and lines) of P into a projective space H to be extendable to an incidencepreserving map from G to H. As a consequence, we obtain conditions for such an embedding to be induced by a semilinear ma...
متن کاملClassical polar spaces (sub–)weakly embedded in projective spaces
In this paper we are concerned with classical polar spaces, i. e. with the set of points and lines of some vector space W on which a non–degenerate (σ, )-hermitian form or pseudo-quadratic form vanishes. To state the Main Theorem we introduce some notation. Let L be a division ring and W be a (left–)vector space over L endowed with a (σ, )–hermitian form or a pseudo–quadratic form q (with assoc...
متن کاملThe geometry of secants in embedded polar spaces
Consider a polar space S weakly embedded in a projective space P. A secant of S is the intersection of the point set of S with a line of P spanned by two non-collinear points of S. The geometry consisting of the points of S and as lines the secants is a so-called Delta space. In this paper we give a characterization of this and some related geometries.
متن کاملPolar Quantization Revisited
A uniied analysis of several polar quantization schemes is developed by focusing on their point densities and inertial prooles and using Bennett's integral to express the mean-squared error. The subsequent analysis is straightforward and leads to new insights into the relationship between polar quantization and Cartesian quantization. With this approach, unrestricted polar quantization, which i...
متن کاملMorphisms of polar spaces
Polar spaces are presented from the point of view of paraprojective spaces. Morphisms are introduced and some immediate categorical aspects are reviewed. The morphisms of polar spaces are then studied in more details and are shown to preserve the spaces’ structure. Finally, it is shown that a morphism of polar spaces can be split into a morphism of nondegenerate polar spaces and a morphism of p...
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ژورنال
عنوان ژورنال: Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial
سال: 2017
ISSN: 1781-6475,1781-6475
DOI: 10.2140/iig.2017.15.31