Function Space-Time Manifolds

Rational Classification of Simple Function Space Components for Flag Manifolds

Let M(X, Y) denote the space of all continuous functions between X and Y and Mf (X, Y) the path component corresponding to a given map f : X ! Y. When X and Y are classical flag manifolds, we prove the components of M(X, Y) corresponding to “simple” maps f are classified up to rational homotopy type by the dimension of the kernel of f in degree two cohomology. In fact, these components are them...

Quantizations of Flag Manifolds and Conformal Space Time

In this letter we work out the deformations of some flag manifolds and of complex Minkowski space viewed as an affine big cell inside G(2, 4). All the deformations come in tandem with a coaction of the appropriate quantum group. In the case of the Minkowski space this allows us to define the quantum conformal group. We also give two involutions on the quantum complex Minkowski space, that respe...

Space-time radial basis function collocation method for one-dimensional advection-diffusion problem

The parabolic partial differential equation arises in many application of technologies. In this paper, we propose an approximate method for solution of the heat and advection-diffusion equations using Laguerre-Gaussians radial basis functions (LG-RBFs). The results of numerical experiments are compared with the other radial basis functions and the results of other schemes to confirm the validit...

Harmonic space and quaternionic manifolds

We find a principle of harmonic analyticity underlying the quaternionic (quaternionKähler) geometry and solve the differential constraints which define this geometry. To this end the original 4n-dimensional quaternionic manifold is extended to a biharmonic space. The latter includes additional harmonic coordinates associated with both the tangent local Sp(1) group and an extra rigid SU(2) group...

Space Forms of Grassmann Manifolds