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Diagram Geometry pp 305–368Cite as

Polar Spaces

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Abstract

We come to one of the central themes in the theory of geometries of spherical Coxeter type. It can be described in various intertwining ways, such as: polarities in projective spaces and their absolutes, (both algebraic and geometric) quadrics in projective spaces, geometries belonging to a diagram of type B n , or polar spaces: line spaces satisfying the property that, for each line of the space, each point is collinear with either one or all points of that line.

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Authors and Affiliations

  1. Dépt. Mathématique, Université Libre de Bruxelles, Académie royale de Belgique, Bruxelles, Belgium

    Francis Buekenhout

  2. Dept. Mathematics & Computer Science, Eindhoven University of Technology, Eindhoven, Netherlands

    Arjeh M. Cohen

Authors
  1. Francis Buekenhout
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  2. Arjeh M. Cohen
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Buekenhout, F., Cohen, A.M. (2013). Polar Spaces. In: Diagram Geometry. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34453-4_7

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