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In mathematics, a Kleinian group is a discrete subgroup of PSL(2, C). The group PSL(2, C) of 2 by 2 complex matrices of determinant 1 modulo its center has several natural representations: as conformal transformations of the Riemann sphere, and as orientation-preserving isometries of 3-dimensional hyperbolic space H3, and as orientation preserving conformal maps of the open unit ball B3 in R3 to itself. Therefore, a Kleinian group can be regarded as a discrete subgroup acting on one of these spaces.

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  • زمرة كلاينية
  • Kleinian group
  • Kleinsche Gruppe
  • Клейнова группа
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  • في الرياضيات, زمرة كلاينية هي زمرة جزئية متقطعة... أسست نظرية الزمر الكلاينية العامة من طرف فيليكس كلاين (1883) وهنري بوانكاريه (1883).
  • In der Mathematik spielen Kleinsche Gruppen eine zentrale Rolle in 3-dimensionaler Topologie, hyperbolischer Geometrie und komplexer Analysis.
  • Клейнова группа — дискретная подгруппагруппы дробно-линейных преобразованийрасширенной комплексной плоскости, являющаяся собственно разрывной. Начало их изучения положено в 1883 году Феликсом Клейном и Анри Пуанкаре.
  • In mathematics, a Kleinian group is a discrete subgroup of PSL(2, C). The group PSL(2, C) of 2 by 2 complex matrices of determinant 1 modulo its center has several natural representations: as conformal transformations of the Riemann sphere, and as orientation-preserving isometries of 3-dimensional hyperbolic space H3, and as orientation preserving conformal maps of the open unit ball B3 in R3 to itself. Therefore, a Kleinian group can be regarded as a discrete subgroup acting on one of these spaces.
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