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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;
Definition source: English Wiktionary via Wiktextract
Qualifier: differential geometry
Examples
- 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
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.
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.
Definition source: English Wiktionary via Wiktextract
Qualifier: differential geometry; more formally
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
The coset space G / H.
Definition source: English Wiktionary via Wiktextract
Usage: broadly
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Named after German mathematician Christian Felix Klein (1849—1925). The concept arose from Klein's Erlangen program (published 1872).
Across languages
Translations
1 source translations are retained for this English entry.
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German:
Kleinsche Geometrie
— type of geometry
