Applying the methods developed in [3], in [4] we have constructed generalized CS attached to the Jacobi group G1 = H1 oSU(1, 1), based on the homogeneous Kähler manifold D 1 = H1/R × SU(1, 1)/U(1) = C 1 × D1. Here D1 denotes the unit disk D1 = {w ∈ C ; |w| < 1}, and Hn is the (2n + 1)-dimensional real Heisenberg-Weyl group with Lie algebra hn. In [4] we have also emphasized that, when expressed...

Let M be a four-dimensional orientable manifold equipped with a Minkowski type metric g and with a polarization. In general relativity such a manifoldM is used as a stage for all physical phenomena. When describing the spin phenomenon M is additionally assumed to be a spin manifold. In this case it admits two spinor bundles: the bundle of Weyl spinors SM and the bundle of Dirac spinors DM (see ...

We prove that for each closed smooth spin 4-manifold M there exists a closed smooth 4-manifold N such that M#N admits a conformally flat Riemannian metric.

We study a class of asymptotically cylindrical Ricci-flat Kähler metrics arising on quasiprojective manifolds. Using the Calabi–Yau geometry and analysis and the Kodaira–Kuranishi–Spencer theory and building up on results of N.Koiso, we show that under rather general hypotheses any local asymptotically cylindrical Ricci-flat deformations of such metrics are again Kähler, possibly with respect t...

We derive the Penrose data for half-flat pp-waves and extend his original construction Weyl spinor of plane waves in terms these data.

We derive a class of variational functionals which arise naturally in conformal geometry. In the special case when the Riemannian manifold is locally conformal flat, the functional coincides with the well studied functional which is the integration over the manifold of the k-symmetric function of the Schouten tensor of the metric on the manifold.

Spectral Methods. The basic idea is to assume that the data lies on a manifold/surface in D-dimensional space, see figure (1) Perform multi-dimensional scaling, or other dimension reduction method, using distances calculated on the manifold, see figure (2). Figure 1. We assume that the data lies on a manifold. This is a surface which is locally flat.