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