Klein geometry
短语词形变化
释义与例句
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1.
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.
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2.
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.
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3.
The coset space G / H.
词源
Named after German mathematician Christian Felix Klein (1849—1925). The concept arose from Klein's Erlangen program (published 1872).
来源：wiktionary