Search results for "Real projective line"

showing 5 items of 5 documents

Area minimizing projective planes on the projective space of dimension 3 with the Berger metric

2016

Abstract We show that, among the projective planes embedded into the real projective space R P 3 endowed with the Berger metric, those of least area are exactly the ones obtained by projection of the equatorial spheres of S 3 . This result generalizes a classical result for the projective spaces with the standard metric.

CollineationComplex projective space010102 general mathematicsMathematical analysisGeneral MedicineFubini–Study metric01 natural sciencesCombinatoricsReal projective line0103 physical sciencesProjective space010307 mathematical physicsProjective plane0101 mathematicsQuaternionic projective spacePencil (mathematics)MathematicsComptes Rendus Mathematique
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Embedding finite linear spaces in projective planes, II

1987

Abstract It is shown that a finite linear space with maximal point degree n + 1 can be embedded in a projective plane of order n, provided that the line sizes are big enough.

Discrete mathematicsLine at infinityFano planeTheoretical Computer ScienceCombinatoricsReal projective lineReal projective planeDuality (projective geometry)Finite geometryProjective spaceDiscrete Mathematics and CombinatoricsProjective planeComputer Science::DatabasesMathematicsDiscrete Mathematics
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Embedding Locally Projective Planar Spaces Into Projective Spaces

1988

We shall show that a 3-dimensional locally projective planar space of finite order n can be embedded into a 3-dimensional projective space of order n, if it has at least n 3 points.

Discrete mathematicsPure mathematicsReal projective lineCollineationProjective unitary groupComplex projective spaceProjective spaceProjective planeQuaternionic projective spacePencil (mathematics)Mathematics
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Embedding linear spaces with two line degrees in finite projective planes

1986

In this paper we shall classify all finite linear spaces with line degrees n and n-k having at most n2+n+1 lines. As a consequence of this classification it follows: If n is large compared with k, then any such linear space can be embedded in a projective plane of order n−1 or n.

Discrete mathematicsPure mathematicsReal projective lineReal projective planeDuality (projective geometry)Finite geometryProjective spaceLine at infinityGeometry and TopologyFano planeProjective planeMathematicsJournal of Geometry
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A Common Characterization of Finite Projective Spaces and Affine Planes

1981

Let S be a finite linear space for which there is a non-negative integer s such that for any two disjoint lines L, L' of S and any point p outside L and L' there are exactly s lines through p intersecting the two lines L and L'. We prove that one of the following possibilities occurs: (i) S is a generalized projective space, and if the dimension of S is at least 4, then any line of S has exactly two points. (ii) S is an affine plane, an affine plane with one improper point, or a punctured projective plane. (iii) S is the Fano-quasi -plane.

Plane curveFano planeTheoretical Computer ScienceCombinatoricsReal projective lineComputational Theory and MathematicsBlocking setReal projective planeFinite geometryDiscrete Mathematics and CombinatoricsProjective spaceGeometry and TopologyProjective planeMathematicsEuropean Journal of Combinatorics
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