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In differential geometry and the study of Lie groups, a parabolic geometry is a homogeneous space G/P which is the quotient of a semisimple Lie group G by a parabolic subgroup P. More generally, the curved analogs of a parabolic geometry in this sense is also called a parabolic geometry: any geometry that is modeled on such a space by means of a Cartan connection.

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  • Parabolic geometry (differential geometry)
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  • In differential geometry and the study of Lie groups, a parabolic geometry is a homogeneous space G/P which is the quotient of a semisimple Lie group G by a parabolic subgroup P. More generally, the curved analogs of a parabolic geometry in this sense is also called a parabolic geometry: any geometry that is modeled on such a space by means of a Cartan connection.
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  • In differential geometry and the study of Lie groups, a parabolic geometry is a homogeneous space G/P which is the quotient of a semisimple Lie group G by a parabolic subgroup P. More generally, the curved analogs of a parabolic geometry in this sense is also called a parabolic geometry: any geometry that is modeled on such a space by means of a Cartan connection.
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