klein geometry
Word Rarity
Rare
Frequency: Zipf frequency 3.49 in modern English
23
Scrabble Score
13
Letters
5
Syllables
11
Unique Chars
Meaning
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
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.
Example Sentences
- "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."
- "The present paper develops the general theory of non-holonomic geometries as generalizations of Klein geometries starting from a set of fundamental assumptions presented in the form of postulates."
- "The kernel of a Klein geometry (G,H) is the largest subgroup K of H that is normal in G. A Klein geometry (G,H) is effective if K#61;1 and locally effective if K is discrete. A Klein geometry is geometrically oriented if G is connected."
- "A careful geometric study of Klein geometries is available in [Sh97, Chapter 4]. Given a Klein geometry (G,H) we may first ask whether all of G is “visible” on G#47;H, i.e. whether the action #92;mathcal#123;l#125; of G on G#47;H is effective. In this case, we call the Klein geometry effective."
Etymology
Named after German mathematician Christian Felix Klein (1849—1925). The concept arose from Klein's Erlangen program (published 1872).
Inflected Forms
Phrases
Cayley-Klein geometry
Frequently Paired Words
Cayley-Klein geometry