A CHARACTERIZATION OF THE REAL PROJECTIVE PLANE

2010 ◽  
Vol 21 (12) ◽  
pp. 1605-1617
Author(s):  
JOËL ROUYER
Keyword(s):  
Projective Plane ◽  
Riemannian Geometry ◽  
Smooth Surface ◽  
Real Projective Plane ◽  
Closed Curves ◽  
Farthest Points ◽  
The Real ◽  
Large Sets

It is proved in this article, that in the framework of Riemannian geometry, the existence of large sets of antipodes (i.e. farthest points) for diametral points of a smooth surface has very strong consequences on the topology and the metric of this surface. Roughly speaking, if the sets of antipodes of diametral points are closed curves, then the surface is nothing but the real projective plane.

Gilles Deleuze's Luminous Philosophy

2020 ◽  
Author(s):  
Hanjo Berressem
Keyword(s):  
Projective Plane ◽  
Visual Arts ◽  
Whole Body ◽  
Literary Studies ◽  
Chronological Order ◽  
Real Projective Plane ◽  
Cinema Studies ◽  
The Real

Providing a comprehensive reading of Deleuzian philosophy, Gilles Deleuze’s Luminous Philosophy argues that this philosophy’s most consistent conceptual spine and figure of thought is its inherent luminism. When Deleuze notes in Cinema 1 that ‘the plane of immanence is entirely made up of light’, he ties this philosophical luminism directly to the notion of the complementarity of the photon in its aspects of both particle and wave. Engaging, in chronological order, the whole body and range of Deleuze’s and Deleuze and Guattari’s writing, the book traces the ‘line of light’ that runs through Deleuze’s work, and it considers the implications of Deleuze’s luminism for the fields of literary studies, historical studies, the visual arts and cinema studies. It contours Deleuze’s luminism both against recent studies that promote a ‘dark Deleuze’ and against the prevalent view that Deleuzian philosophy is a philosophy of difference. Instead, it argues, it is a philosophy of the complementarity of difference and diversity, considered as two reciprocally determining fields that are, in Deleuze’s view, formally distinct but ontologically one. The book, which is the companion volume toFélix Guattari’s Schizoanalytic Ecology, argues that the ‘real projective plane’ is the ‘surface of thought’ of Deleuze’s philosophical luminism.

The Real Projective Plane

1993 ◽  
Author(s):  
H. S. M. Coxeter ◽  
George Beck
Keyword(s):  
Projective Plane ◽  
Real Projective Plane ◽  
The Real

scholarly journals Homography in ℝℙ

2016 ◽  
Vol 24 (4) ◽  
pp. 239-251 ◽  
Author(s):  
Roland Coghetto
Keyword(s):  
Projective Space ◽  
Projective Plane ◽  
Projective Spaces ◽  
Invertible Matrix ◽  
Real Projective Plane ◽  
The Real ◽  
Mizar Mathematical Library ◽  
Plücker Relation

Summary The real projective plane has been formalized in Isabelle/HOL by Timothy Makarios [13] and in Coq by Nicolas Magaud, Julien Narboux and Pascal Schreck [12]. Some definitions on the real projective spaces were introduced early in the Mizar Mathematical Library by Wojciech Leonczuk [9], Krzysztof Prazmowski [10] and by Wojciech Skaba [18]. In this article, we check with the Mizar system [4], some properties on the determinants and the Grassmann-Plücker relation in rank 3 [2], [1], [7], [16], [17]. Then we show that the projective space induced (in the sense defined in [9]) by ℝ3 is a projective plane (in the sense defined in [10]). Finally, in the real projective plane, we define the homography induced by a 3-by-3 invertible matrix and we show that the images of 3 collinear points are themselves collinear.

The Real Projective Plane

1956 ◽  
Vol 40 (332) ◽  
pp. 153
Author(s):  
D. Pedoe ◽  
H. S. M. Coxeter
Keyword(s):  
Projective Plane ◽  
Real Projective Plane ◽  
The Real

scholarly journals Straight line arrangements in the real projective plane

1998 ◽  
Vol 20 (2) ◽  
pp. 155-161 ◽  
Author(s):  
D. Forge ◽  
J. L. Ramírez Alfonsín
Keyword(s):  
Projective Plane ◽  
Real Projective Plane ◽  
The Real ◽  
Line Arrangements ◽  
Straight Line

FIRST BETTI NUMBERS OF ABELIAN COVERINGS OF THE COMPLEX PROJECTIVE PLANE BRANCHED OVER LINE CONFIGURATIONS

2000 ◽  
Vol 09 (02) ◽  
pp. 271-284 ◽  
Author(s):  
IKUO TAYAMA
Keyword(s):  
Projective Plane ◽  
Real Line ◽  
General Position ◽  
Betti Numbers ◽  
Complex Projective Plane ◽  
The Real ◽  
Complex Projective

We prove the following results concerning the first Betti numbers of abelian coverings of CP2 branched over line configurations: (1) An estimate of the first Betti numbers. (2) A characterization of central and general position line configurations in terms of the first Betti numbers of abelian coverings. (3) The first Betti numbers of the abelian coverings of the real line configurations up to 7 components.

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