The purpose of this note is to show that the construction of the C-algebra for the space-time uncertainty relations which was introduced by Doplicher, Fredenhagen and Roberts [2,3,4] fits comfortably into the deformation quantization framework developed in [5]. This has the mild advantages that one can work directly with functions on space-time rather than with their Fourier transforms, the tre...

In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions C∞(M) on a Kähler manifold M . In this setup one interprets M as the phase space itself, equipped with the Poisson brackets inherited from the Kähler 2-form. We compare the geometric quantization framework with several deformation quantization approaches. We find that the balanc...

Let A be a star product on a symplectic manifold (M,ω0), 1 t [ω] its Fedosov class, where ω is a deformation of ω0. We prove that for a complex polarization of ω there exists a commutative subalgebra, O, in A that is isomorphic to the algebra of functions constant along the polarization. Let F (A) consists of elements of A whose commutator with O belongs to O. Then, F (A) is a Lie algebra which...

in this study, 2n -dimensional (n > 2) generalized conformally recurrent kaehlerian weyl spaces andgeneralized conharmonicaly recurrent kaehlerian weyl spaces are defined. it is proved that a kaehlerian weylspace is generalized conformally recurrent if and only if it is generalized recurrent.also, it is shown that akaehlerian weyl space will be generalized recurrent if and only if it is general...

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...

Motivated by the invariance of current representations of quantum gravity under diffeomorphisms much more general than isometries, the Haag-Kastler setting is extended to manifolds without metric background structure. First, the causal structure on a differentiable manifold M of arbitrary dimension (d+1 > 2) can be defined in purely topological terms, via cones (C-causality). Then, the general ...

In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...

We obtain an algorithm computing the Chern-Schwartz-MacPherson (CSM) classes of Schubert cells in a generalized flag manifold G{B. In analogy to how the ordinary divided difference operators act on Schubert classes, each CSM class of a Schubert class is obtained by applying certain Demazure-Lusztig type operators to the CSM class of a cell of dimension one less. These operators define a represe...

A compact quasi-regular Sasakian manifold M is foliated by onedimensional leaves and the transverse space of this characteristic foliation is necessarily a compact Kähler orbifold Z. In the case when the transverse space Z is also Einstein the corresponding Sasakian manifold M is said to be Sasakian η-Einstein. In this article we study η-Einstein geometry as a class of distinguished Riemannian ...

the objective of this work was to develop a new design of an intake manifold through a 1d simulation. it is quite familiar that a duly designed intake manifold is essential for the optimal performance of an internal combustion engine. air flow inside the intake manifold is one of the important factors, which governs the engine performance and emissions. hence the flow phenomenon inside the inta...