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

exceptional spaces, namely EIII and EVII. The non-compact Hermitian symmetric spaces can be realized as bounded symmetric domains in complex vector spaces. A Riemannian...

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

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...

the bilinear form is called symmetric, and for ε = −1 is called skew-symmetric. Let V be the three dimensional vector space over the finite field F = GF(q2)...

is Hermitian}}\quad \iff \quad A={\overline {A^{\mathsf {T}}}}.} Hermitian matrices can be understood as the complex extension of real symmetric matrices...

operator (sometimes a symmetric operator, sometimes a symmetric densely defined operator, sometimes a self-adjoint operator) Hermitian polynomials, a classical...

the complex plane is also a Hermitian symmetric space; this gives the complete list of irreducible Hermitian symmetric spaces. The four families are the...

be symmetric spaces. Over the complex numbers, the corresponding flag manifolds are the Hermitian symmetric spaces. Over the real numbers, an R-space is...

{(A)}} is skew-symmetric and the imaginary part ℑ ( A ) {\displaystyle \Im {(A)}} is symmetric. If A {\displaystyle A} is skew-Hermitian, then A k {\displaystyle...

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...

defined to be the symmetric map ⟨ x , y ⟩ = x y {\displaystyle \langle x,y\rangle =xy} (rather than the usual conjugate symmetric map ⟨ x , y ⟩ = x y...

{\displaystyle \ M\ } is symmetric or Hermitian, and all its eigenvalues are real and positive.   M   {\displaystyle \ M\ } is symmetric or Hermitian, and all its...

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...

provided by the Hermitian symmetric spaces of compact type, such as Grassmannians. The natural Kähler metric on a Hermitian symmetric space of compact type...

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

any compact hermitian symmetric space is simply connected and can be written as a direct product of irreducible hermitian symmetric spaces Gi / Ki with...

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...

analogue of a modular curve that arises as a quotient variety of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined...

A.} The densely defined operator A {\displaystyle A} is called symmetric (or Hermitian) if A ⊆ A ∗ {\displaystyle A\subseteq A^{*}} , i.e., if Dom ⁡ A...

the four-dimensional Euclidean dot product. This inner product is Hermitian symmetric, which means that the result of interchanging z and w is the complex...

groups on the list and certain symmetric spaces, namely the hermitian symmetric spaces and the quaternion-Kähler symmetric spaces. The relationship is particularly...

manifold with a smoothly varying Hermitian inner product on each (holomorphic) tangent space. One can also define a Hermitian manifold as a real manifold with...

compactify it. The Baily–Borel compactification of a quotient of a Hermitian symmetric space. The wonderful compactification of a quotient of algebraic groups...

Kuga (1966), is a fiber space whose fibers are abelian varieties and whose base space is an arithmetic quotient of a Hermitian symmetric space. Kuga, Michio (1966)...

transformation of the space. If V {\displaystyle V} is finite-dimensional, then its dimension must necessarily be even since every skew-symmetric, hollow matrix...

for differential systems Isotropic line CAT(k) space Einstein – Cartan theory Hermitian symmetric space Moving frame Pseudogroup Pure spinor O'Connor,...

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

by Max Koecher in his Jordan algebraic approach to Hermitian symmetric spaces and bounded symmetric domains of tube type. Their functorial properties allow...

Baily–Borel compactification is a compactification of a quotient of a Hermitian symmetric space by an arithmetic group, introduced by Walter L. Baily and Armand...