Pascal-Brianchon Sets in Pappian Projective Planes Pascal-Brianchon Sets in Pappian Projective Planes
نویسنده
چکیده
It is well-known that Pascal and Brianchon theorems characterize conics in a Pappian projective plane. But, using these theorems and their modifications we shall show that the notion of a conic (or better a Pascal-Brianchon set) can be defined without any use of theory of projectivities or of polarities as usually.
منابع مشابه
Sharply 2-transitive groups of projectivities in generalized polygons
The group of projectivities of (a line of) a projective plane is always 3-transitive. It is well known that the projective planes with a sharply 3-transitive group of projectivities are classi/ed: they are precisely the Pappian projective planes. It is also well known that the group of projectivities of a generalized polygon is 2-transitive. Here, we classify all generalized quadrangles, all /n...
متن کاملOn Sets of Lines Corresponding to Affine Spaces
1. Given a 3-dimensional Pappian projective space, it is well known that the Grassmannian which is representing its set of lines is a quadric (called the Pltcker quadric) in a 5-dimensional projective space. The link between the set of lines and the Pltcker quadric is the bijective Klein map g. Under g pencils of lines become lines of the Pltcker quadric. Cf. e.g. [5,287], [15,28], [16,13], [20...
متن کاملOn Epimorphisms and Projectivities of Projective Planes1
Given an epimorphism φ: Π → Π' between projective planes Π and Π', it is an open question how the groups of projectivities of Π and Π' (regarded as permutation groups on projective lines) are related. Within this note we will not answer this sophisticated and hard problem in full, but we will address the question to which extend the projectivities of Π induce permutations on the lines of Π ' wh...
متن کاملMappings of the Sets of Invariant Subspaces of Null Systems
Let P and P ′ be (2k + 1)-dimensional Pappian projective spaces. Let also f : P → P∗ and f ′ : P ′ → P ′∗ be null systems. Denote by Gk(f) and Gk(f ′) the sets of all invariant k-dimensional subspaces of f and f ′, respectively. In the paper we show that if k ≥ 2 then any mapping of Gk(f) to Gk(f ′) sending base subsets to base subsets is induced by a strong embedding of P to P ′. MSC 2000: 51M...
متن کاملFinite Hjelmslev Planes with New Integer Invariants
Projective Hjelmslev planes (PH-planes) are a generalization of projective planes in which each point-pair is joined by at least one line and, dually, each line-pair has a nontrivial intersection. Multiply joined points (and multiply intersecting lines) are called neighbor points (and neighbor lines). By hypothesis, the neighbor relations of a PH-plane A are equivalence relations which induce a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006