We show that any non-Kähler, almost Kähler 4-manifold for which both the Ricci and the Weyl curvatures have the same algebraic symmetries as they have for a Kähler metric is locally isometric to the (only) proper 3-symmetric four-dimensional space. Mathematics Subject Classifications (2000): Primary 53B20, 53C25.

We build blowing-up solutions for a supercritical perturbation of the Yamabe problem on manifolds with umbilic boundary, provided dimension manifold is n ≥ 8 and that Weyl tensor W g not vanishing ∂ M .

The assumption in the main result of [2] is removed Let G be a Lie group which acts isometrically on a Riemannian manifold M . A section of the Riemannian G-manifold M is a closed submanifold Σ which meets each orbit orthogonally. In this situation the trace on Σ of the G-action is a discrete group action by the generalized Weyl group W (Σ) = NG(Σ)/ZG(Σ), where NG(Σ) := {g ∈ G : g.Σ = Σ} and ZG...

This paper concerns the topology of the isospectral real manifold of the sl(N) periodic Toda lattice consisting of 2 different systems. The solutions of those systems contain blow-ups, and the set of those singular points defines a devisor of the manifold. Then adding the divisor, the manifold is compactified as the real part of the (N − 1)dimensional Jacobi variety associated with a hyperellip...

The spectrum (of the Dirichlet Laplacian) of non-compact, non-complete Riemannian manifolds is much less understood than their compact counterparts. In particular it is often not even known whether such a manifold has any discrete spectra. In this article, we will prove that a certain type of non-compact, non-complete manifold called the quantum tube has non-empty discrete spectrum. The quantum...

Resonance asymptotics for asymptotically hyperbolic manifolds with warped-product ends By Pascal Philipp We study the spectral theory of asymptotically hyperbolic manifolds with ends of warped-product type. Our main result is an upper bound on the resonance counting function, with a geometric constant expressed in terms of the respective Weyl constants for the core of the manifold and the base ...

• Topology of G/T : Flag manifolds G/T have cohomology only in even degrees, with Euler characteristic the degree of the Weyl group. The Euler characteristic can be calculated by a Lefschetz fixed point argument (see Adams [1], pgs. 90-92 for this). Identifying the flag manifold with a co-adjoint orbit, there is a Morse theory calulation of the cohomology that goes back to Bott, for an outline ...

We first introduce the Wigner-Weyl-Moyal formalism for a theory whose phase-space is an arbitrary Lie algebra. We also generalize to quantum Lie algebras and to supersymmetric theories. It turns out that the non-commutativity leads to a deformation of the classical phase-space: instead of being a vector space it becomes a manifold, the topology of which is given by the commutator relations. It ...

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 ...