Category
page 1Homogeneous spaces
sphere
A sphere (from Ancient Greek , ) is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance from a given point in three-dimensional space. That given point is the center of the sphere, and the distance is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians.
Euclidean space
generalization of Euclidean geometry to higher-dimensional vector spaces
Erlangen program
research program on the symmetries of geometry
homogeneous space
topological space that is the space of cosets of a topological group
hyperbolic space
homogeneous space that has a constant negative curvature (not any hyperbolic manifold)
symmetric space
pseudo-Riemannian manifold whose symmetry group contains an inversion symmetry about every point
Stiefel manifold
the manifold of all orthonormal k-frames in n-dimensional Euclidean space