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.