This paper is a sequel to our previous papers [NT1], [NT2], which deal with the splitting phenomena and Hasse principle for

homogeneous spaces over global fields and also with the extensions of known Hasse principles over global fields to the case of infinite global fields (cf.

However, the converse is not true, even in the category of

homogeneous spaces [12].

His topics include groups and

homogeneous spaces, the extended Fillmore-Springer-Cnops construction, the indefinite product space of cycles, metric invariants in upper half-planes, conformal unit disk, and unitary rotations.

Specifically, we are going to study such problems as the local index formula, equivariance of Dirac operators with respect to the dual group action (with an eye towards the Baum-Connes conjecture for discrete quantum groups), construction of Dirac operators on quantum

homogeneous spaces, structure of quantized C*-algebras of continuous functions, computation of dual cohomology of compact quantum groups.

Because in reality there does not exist isolated

homogeneous spaces, but a mixture of them, interconnected, and each having a different structure.

He discusses special and general relativity and the cosmological versions of both, properties of the gravitational field, particle production in five-dimensional cosmological relativity, properties of gravitational waves in an expanding universe, spiral galaxy rotation curves in the Brane world theory in five dimensions, testing cosmological general relativity against high redshift observations,

homogeneous spaces and Bianchi classifications, and similar topics.

In general, research on visual perception of space is accomplished on

homogeneous spaces, characterized by presentation of isolated stimuli in front of observers in order to investigate functional aspects of visual space.

Hwang, Rigidity of rational

homogeneous spaces, in International Congress of Mathematicians.

His topics include invariant connections on reductive

homogeneous spaces, finite order isometries and twistor spaces, vertically harmonic maps and harmonic sections of submersions, generalized harmonic maps, and generalized harmonic maps into f-manifolds and into reductive

homogeneous spaces.

Because in reality there do not exist isolated

homogeneous spaces, but a mixture of them, interconnected, and each having a different structure.

Some topics examined are superrigidity and first applications, locally

homogeneous spaces, and orbit equivalence.

It focuses on the use of this method to compute local geometric invariants for curves and surfaces in various three-dimensional

homogeneous spaces, including Euclidean, Minkowski, affine, and projective spaces.