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Klein geometry

noun

Etymology

Named after German mathematician Christian Felix Klein (1849—1925). The concept arose from Klein's Erlangen program (published 1872).

Definitions

  1. A type of geometry (mathematical object representing a space and its spatial…

    A type of geometry (mathematical object representing a space and its spatial relationships); a homogeneous space X together with a symmetry group which represents the group action on X of some Lie group;

    • Given a Klein geometry (G,H), the group G is called the principal group and G#47;H is called the space of the geometry.
    • The space of a Klein geometry is a smooth manifold of dimension #92;operatorname#123;dim#125;G-#92;operatorname#123;dim#125;H.
    • The present paper develops the general theory of non-holonomic geometries as generalizations of Klein geometries starting from a set of fundamental assumptions presented in the form of postulates.

  2. The coset space G / H.

The neighborhood

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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA