B. Fedosov has given a simple and very natural construction of a deformation quantization for any symplectic manifold, using a flat connection on the bundle of formal Weyl algebras associated to the tangent bundle of a symplectic manifold. The connection is obtained by affinizing, nonlinearizing, and iteratively flattening a given torsion free symplectic connection. In this paper, a classical a...

The formality theorem for Hochschild chains of the algebra of functions on a smooth manifold gives us a version of the trace density map from the zeroth Hochschild homology of a deformation quantization algebra to the zeroth Poisson homology. We propose a version of the algebraic index theorem for a Poisson manifold which is based on this trace density map. 1991 MSC: 19K56, 16E40.

We give a classification of polarized deformation quantizations on a symplectic manifold with a (complex) polarization. Also, we establish a formula which relates the characteristic class of a polarized deformation quantization to its Fedosov class and the Chern class of the polarization.

TIn this article, the M-projective and Weyl curvature tensors on a normal paracontact metric manifold are discussed. For manifolds, pseudosymmetric cases investigated some interesting results obtained. We show that semisymmetric is of constant sectional curvature. also obtain an $\eta$-Einstein manifold. Finally, we support our topic with example.

Starting from a real analytic surface ℳ with conformal Cartan connection A. Bor´owka constructed minitwistor space of an asymptotically hyperbolic Einstein–Weyl manifold being the boundary. In this article, starting symmetry connection, we prove that symmetries on can be extended to obtained manifold.

We investigate discrete groups G of isometries of a complete connected Riemannian manifold M which are generated by reflections, in particular those generated by disecting reflections. We show that these are Coxeter groups, and that the the orbit space M/G is isometric to a Weyl chamber C which is a Riemannian manifold with corners and certain angle conditions along intersections of faces. We c...

In ([1]), T. Adati and K. Matsumoto defined para-Sasakian and special para-Sasakian manifolds which are considered as special cases of an almost paracontact manifold introduced by I. Sato and K. Matsumoto ([10]). In the same paper, the authors studied conformally symmetric para-Sasakian manifolds and they proved that an ndimensional (n>3) conformally symmetric para-Sasakian manifold is conforma...

Suppose that (Mn, g) is an asymptotically flat Riemannian spin manifold of positive scalar curvature. The positive mass theorem [1, 2, 3] states that the total mass of the manifold is always positive, and is zero if and only if the manifold is flat. This result suggests that there should be an inequality which bounds the Riemann tensor in terms of the total mass and implies that curvature must ...

Lie derivatives arise in studying continuous symmetries of various geometric structures on manifolds. They are also used in symmetry analysis of ordinary and partial differential equations (see [1]). In general relativity the bundle of Weyl spinors SM is a special geometric structure built over the space-time manifold M . The main goal of this paper is to clarify the procedure of applying Lie d...