Symmetric space
Encyclopedia
A symmetric space
is, in differential geometry and representation theory, a smooth manifold whose group of symmetries contains an "inversion symmetry" about every point. Examples include:
In topology, symmetric space may also refer to:
Symmetric space
A symmetric space is, in differential geometry and representation theory, a smooth manifold whose group of symmetries contains an "inversion symmetry" about every point...
is, in differential geometry and representation theory, a smooth manifold whose group of symmetries contains an "inversion symmetry" about every point. Examples include:
- Riemannian symmetric spaceRiemannian symmetric spaceIn differential geometry, representation theory and harmonic analysis, a symmetric space is a smooth manifold whose group of symmetries contains an inversion symmetry about every point. There are two ways to formulate the inversion symmetry, via Riemannian geometry or via Lie theory...
- Hermitian symmetric spaceHermitian symmetric spaceIn mathematics, a Hermitian symmetric space is a Kähler manifold M which, as a Riemannian manifold, is a Riemannian symmetric space. Equivalently, M is a Riemannian symmetric space with a parallel complex structure with respect to which the Riemannian metric is Hermitian...
- Quaternion-Kähler symmetric space
- Weakly symmetric spaceWeakly symmetric spaceIn mathematics, a weakly symmetric space is a notion introduced by the Norwegian mathematician Atle Selberg in the 1950s as a generalisation of symmetric space, due to Élie Cartan. Geometrically the spaces are defined as complete Riemannian manifolds such that any two points can be exchanged by an...
In topology, symmetric space may also refer to:
- R0 space, a topological space in which two topologically distinguishable points can be separated