Parabolic geometry

Parabolic geometry may refer to:

Euclidean geometry, where Euclidean space is viewed as the natural representation space of the group of Euclidean motions $E(n) = O(n) \ltimes \mathbb{R}^n$
The geometry of a Riemannian manifold admitting no positive Green's function
Parabolic geometry (differential geometry): The homogeneous space defined by a semisimple Lie group modulo a parabolic subgroup, or the curved analog of such a space

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