curvature −1) is a locally symmetric space but not a symmetric space. Every lens space is locally symmetric but not symmetric, with the exception of L (...

Riemannian symmetric space Hermitian symmetric space Quaternion-Kähler symmetric space Weakly symmetric space In topology, symmetric space may also refer...

notion of Riemannian symmetric space from real manifolds to complex manifolds. Every Hermitian symmetric space is a homogeneous space for its isometry group...

computational complexity theory, SL (Symmetric Logspace or Sym-L) is the complexity class of problems log-space reducible to USTCON (undirected s-t connectivity)...

anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. Anti-de Sitter space and de Sitter space are named...

space is also called an accessible space or a space with Fréchet topology and an R0 space is also called a symmetric space. (The term Fréchet space also...

connected symmetric spaces. (For example, the universal cover of a real projective plane is a sphere.) Second, the product of symmetric spaces is symmetric, so...

manifold and the corresponding symmetric spaces are called symmetric R-spaces. A flag in a finite dimensional vector space V over a field F is an increasing...

bilinear form to be symmetric if B(v, w) = B(w, v) for all v, w in V; alternating if B(v, v) = 0 for all v in V; skew-symmetric or antisymmetric if B(v...

weakly symmetric space is a notion introduced by the Norwegian mathematician Atle Selberg in the 1950s as a generalisation of symmetric space, due to...

and is maximally symmetric. Every maximally symmetric space has constant curvature. The Riemann curvature tensor of de Sitter space is given by R ρ σ...

to be locally symmetric. This property nearly characterizes symmetric spaces; Élie Cartan proved in the 1920s that a locally symmetric Riemannian manifold...

the Siegel upper half-space of degree g (or genus g) (also called the Siegel upper half-plane) is the set of g × g symmetric matrices over the complex...

quaternion-Kähler symmetric space or Wolf space is a quaternion-Kähler manifold which, as a Riemannian manifold, is a Riemannian symmetric space. Any quaternion-Kähler...

the symmetric space G / K is the direct product of the two kinds of symmetric spaces Gi / Ki or H × H / H. Non-simply connected symmetric space of compact...

{\displaystyle (0,\ldots ,0)} . Symmetric space: Hyperbolic n {\displaystyle n} -space can be realised as the symmetric space of the simple Lie group S O...

although it is most commonly taken to be either a Lie group or a symmetric space. The model may or may not be quantized. An example of the non-quantized...

number is generic for maximally symmetric spaces. Maximally symmetric spaces can be considered as sub-manifolds of flat space, arising as surfaces of constant...

a symmetric matrix is a square matrix that is equal to its transpose. Formally, A  is symmetric ⟺ A = A T . {\displaystyle A{\text{ is symmetric}}\iff...

That is, it satisfies the condition A  skew-symmetric ⟺ A T = − A . {\displaystyle A{\text{ skew-symmetric}}\quad \iff \quad A^{\textsf {T}}=-A.} In terms...

Complex projective space carries a (Kähler) metric, called the Fubini–Study metric, in terms of which it is a Hermitian symmetric space of rank 1. Complex...

R=0.} A simply connected Riemannian manifold is locally symmetric if it is a symmetric space. From the Cartan–Ambrose–Hicks theorem, we have: Theorem:...

the metric): in particular, it is a CAT(-1/4) space. Complex hyperbolic spaces are also the symmetric spaces associated with the Lie groups P U ( n , 1 )...

was introduced by Élie Cartan (1926) in order to study and classify symmetric spaces. It was not until much later that holonomy groups would be used to...

the antipodal map. A symmetric space is a Riemannian manifold with an isometric reflection across each point. Symmetric spaces play an important role...

symmetric cone is a noncompact Hermitian symmetric space of tube type. All the algebraic and geometric structures associated with the symmetric space...

characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric algebra on V. A related concept is that...

programme symmetric space space form Maurer–Cartan form Examples hyperbolic space Gauss–Bolyai–Lobachevsky space Grassmannian Complex projective space Real...

compact subgroup is a symmetric space and so the theory of automorphic forms is intimately related to harmonic analysis on symmetric spaces. Before the development...

{\displaystyle f.} The most commonly encountered symmetric functions are polynomial functions, which are given by the symmetric polynomials. A related notion is alternating...