symmetric space


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symmetric space

[sə′me·trik ′spās]
(mathematics)
A differentiable manifold which has a differentiable multiplication operation that behaves similarly to the multiplication of a complex number and its conjugate.
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Section 3 is devoted to the Hamiltonian formalism of a general spherically symmetric space time.
The flow field is not symmetric space. So, especially, the secondary vortex flows close to the cylinder outlet occur, which are three-dimensional and include rotary velocity.
A symmetric 2-form on a compact symmetric space (X, g) satisfies the zero-energy condition if all its integrals along the closed geodesics of X vanish.
Then K is a maximal compact subgroup of G and G/K is a Riemannian symmetric space.
If for each [epsilon] > 0 and x [member of] X, the set B(x, [epsilon]) is a neighborhood of x due to the topology [T.sub.d], then a symmetric space d is a semi-metric.
Also, [M.sup.n] is called a locally symmetric space if the curvature tensor R of [M.sup.n] satisfies [nabla]R = 0.
Hence we can discuss Hermitian locally symmetric space [GAMMA]\D.
As expected by (X, d), we denote a nonempty set X equipped with a symmetric d on X and call it a symmetric space. The spaces (X, d) in which limiting points are defined in the usual way is also sometime called an E-space.
Let (X, d) be a symmetric space with symmetric d and D [subset or equal to] X.
Let G/K be a non-compact irreducible Hermitian symmetric space. Then, K has a one-dimensional center, and hence the commutator subgroup [K.sup.s] := [K, K] is of codimension one in K.
van den Ban, Invariant differential operators on a semisimple symmetric space and finite multiplicities in a Plancherel formula, Ark.
and Yukio FUJIKI Classification of irreducible symmetric spaces which admit standard compact Clifford Klein forms Koichi TOJO Hypertranscendence of the multiple sine function for a complex period Masaki KATO Above two, communicated by Masaki KASHIWARA, M.J.A.

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