We investigate the Spin(7) holonomy metric of cohomogeneity one with the principal orbit SU(3)/U(1). A choice of U(1) in the two dimensional Cartan subalgebra is left as free and this allows manifest Σ3 = W (SU(3)) (= the Weyl group) symmetric formulation. We find asymptotically locally conical (ALC) metrics as octonionic gravitational instantons. Complex projective space CP(2) that is a supers...

The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether the...

In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize standard 4-sphere. We obtain a gap theorem, for Yamabe positive scalar curvature $L^2$ norm Weyl tensor metric suitably small, establish monotonic decay $L^p$ certain $p>2$ reduced along normalized flow, converging exponentially to

Our topological setting is a smooth compact manifold of dimension two or higher with boundary. Although this underlying structure smooth, the Riemannian metric tensor only assumed to be bounded and measurable. This known as rough manifold. For large class boundary conditions we demonstrate Weyl law for asymptotics eigenvalues Laplacian associated metric. Moreover, obtain eigenvalue weighted Lap...

In this letter we deene a new state on the Weyl algebra of the Klein-Gordon eld on Robertson-Walker spacetimes. This state approximates a thermal equilibrium state and opens the possibility to do quantum statistical mechanics on expanding universes. We explain why this state is believed to be a physically relevant state in the framework of algebraic quantum eld theory. The methods used in the p...

An exact but simple general relativistic model for the gravitational field of active galactic nuclei is constructed, based on the superposition in Weyl coordinates of a black hole, a Chazy-Curzon disk and two rods, which represent matter jets. The influence of the rods on the matter properties of the disk and on its stability is examined. We find that in general they contribute to destabilize t...

It has been demonstrated, in a number of special situations, that the spin coefficients of a canonical spinor dyad can be used to define a Lanczos potential of the Weyl curvature spinor. In this paper we explore some of these potentials and show that they can be defined directly from the spinor dyad in a very simple way, but that the results do not generalize significantly, in any direct manner...

We develop a global twistor correspondence for pseudo-Riemannian conformal structures of signature (++−−) with self-dual Weyl curvature. Near the conformal class of the standard indefinite product metric on S2 × S2, there is an infinitedimensional moduli space of such conformal structures, and each of these has the surprising global property that its null geodesics are all periodic. Each such c...

We present the explicit metric forms for higher dimensional vanishing scalar invariant (V SI) Lorentzian spacetimes. We note that all of the V SI spacetimes belong to the higher dimensional Kundt class. We determine all of the V SI spacetimes which admit a covariantly constant null vector, and we note that in general in higher dimensions these spacetimes are of Ricci type III and Weyl type III....