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...

In this paper we propose a method to remesh non-manifold surfaces with triangles as equilateral as possible. We adapt an existing Voronoi based remeshing framework to recover the topology of non-manifold surfaces and their boundaries. The input of the procedure is a non-manifold triangulated surface constituted of several connected components representing geological interfaces (faults, horizons...

A Lorentzian manifold is defined here as a smooth pseudoRiemannian manifold with a metric tensor of signature (2n + 1, 1). A Robinson manifold is a Lorentzian manifold M of dimension > 4 with a subbundle N of the complexification of TM such that the fibers of N → M are maximal totally null (isotropic) and [SecN,SecN ] ⊂ SecN . Robinson manifolds are close analogs of the proper Riemannian, Hermi...

We define integrable, big-isotropic structures on a manifold M as subbundles E ⊆ T M ⊕ T * M that are isotropic with respect to the natural, neutral metric g of T M ⊕ T * M , closed by Courant brackets and such that, if E ′ is the g-orthogonal bundle, the Courant brackets [X , Y], X ∈ ΓE, Y ∈ ΓE ′ , belong to ΓE ′. We give the interpretation of such a structure by objects of M , we discuss the ...

In this paper, the segmentation problem is formulated as a problem of segmenting a Riemannian manifold. The image domain is endowed with an anisotropic metric and its segmentation is obtained by thresholding the second eigenvector of the Laplace-Beltrami operator on the Riemannian manifold so defined. The formulation is an analytic analog of a recently proposed approach to segmentation based on...

We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green’s function of an isotropic diffusion equation on a manifold is analytically represented using the eigenfunctions of the Laplace-Beltraimi operator. The Green’s function is then used in explicitly constructing heat kernel smoothing as a series expansion of the eigenfunctions. Unlike many previous ...