Parabolic geometry
Encyclopedia
Parabolic geometry may refer to:
- Euclidean geometryEuclidean geometryEuclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...
, where Euclidean space is viewed as the natural representation space of the group of Euclidean motionsEuclidean groupIn mathematics, the Euclidean group E, sometimes called ISO or similar, is the symmetry group of n-dimensional Euclidean space...
- The geometry of a Riemannian manifoldRiemannian manifoldIn Riemannian geometry and the differential geometry of surfaces, a Riemannian manifold or Riemannian space is a real differentiable manifold M in which each tangent space is equipped with an inner product g, a Riemannian metric, which varies smoothly from point to point...
admitting no positive Green's functionGreen's functionIn mathematics, a Green's function is a type of function used to solve inhomogeneous differential equations subject to specific initial conditions or boundary conditions... - Parabolic geometry (differential geometry)Parabolic geometry (differential geometry)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...
: The homogeneous space defined by a semisimple Lie group modulo a parabolic subgroup, or the curved analog of such a space