Noun
(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;(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.
Given a Klein geometry
(
G
,
H
)
{\displaystyle (G,H)}
, the group
G
{\displaystyle G}
is called the principal group and
G
/
H
{\displaystyle G/H}
is called the space of the geometry.
The space of a Klein geometry is a smooth manifold of dimension
dim
G
−
dim
H
{\displaystyle \operatorname {dim} G-\operatorname {dim} H}
.
(loosely) The coset space G / H.
Source: en.wiktionary.org