Klein geometries

Noun

Klein geometry (plural Klein geometries)

1. (differential geometry) 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.
2. (differential geometry, more formally) an ordered pair (G, H), where G is a Lie group and H a closed Lie subgroup of G such that the left coset space G / H is connected.
3. (broadly) The coset space G / H.