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...

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...

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

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...

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...

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...

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

In mathematical physics, n-dimensional de Sitter space (often denoted dSn) is a maximally symmetric Lorentzian manifold with constant positive scalar curvature...

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...

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...

{\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...

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 )...

it satisfies the condition: p. 38  A  skew-symmetric ⟺ A T = − A . {\displaystyle A{\text{ skew-symmetric}}\quad \iff \quad A^{\textsf {T}}=-A.} In terms...

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

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...

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...

Boolean ring, with symmetric difference as the addition of the ring and intersection as the multiplication of the ring. The symmetric difference is equivalent...

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

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...

algebra is symmetric in A and B, despite the original construction not being symmetric, though Vinberg's symmetric method gives a symmetric construction...

drawbacks of symmetric-key encryption, in comparison to public-key encryption (also known as asymmetric-key encryption). However, symmetric-key encryption...

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...

just symmetric forms when "bilinear" is understood. Symmetric bilinear forms on finite-dimensional vector spaces precisely correspond to symmetric matrices...

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...

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:...

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

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

{\displaystyle K} and X = G / K {\displaystyle X=G/K} is the associated symmetric space the conjugacy classes in Γ {\displaystyle \Gamma } can be described...