Klein geometry
Klein geometry noun: 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;.
Noun
Klein geometry (plural Klein geometries)
- 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.
- 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.
- The coset space G / H.
Forms of Klein geometry
| plural | Klein geometries |
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Origin of Klein geometry
Named after German mathematician Christian Felix Klein (1849—1925). The concept arose from Klein's Erlangen program (published 1872).
Questions about Klein geometry
- What does Klein geometry mean?
- Klein geometry means 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;.
- What part of speech is Klein geometry?
- Klein geometry is a noun.
- What is the plural of Klein geometry?
- The plural of Klein geometry is Klein geometries.
Words near Klein geometry in the dictionary
Source and license
Adapted from Wiktionary: Klein geometry (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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Cite this entry: “Klein geometry.” Word.ws, https://word.ws/klein_geometry. Based on Wiktionary, CC BY-SA 4.0.