English Dictionary

Klein geometry

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;

Klein geometry studies the properties of geometric objects that are invariant under a group of transformations.

意味（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/H is called the space of the geometry.

意味（2）

(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.

意味（3）

(loosely) The coset space G / H.