Finsler and Lagrange spaces can be equivalently represented as almost Kähler manifolds endowed with a metric compatible canonical distinguished connection structure generalizing the Levi Civita connection. The goal of this paper is to perform a natural Fedosov– type deformation quantization of such geometries. All constructions are canonically derived for regular Lagrangians and/or fundamental ...

We introduce a torsion free linear connection on a hypersurface in a Sasakian manifold on which we have defined in natural way a CR-structure of CR-codimension 2. We study the curvature properties of this connection and we give some interesting examples.

An algebraic approach to graph theory can be useful in numerous ways. There is a relatively natural intersection between the fields of algebra and graph theory, specifically between group theory and graphs. Perhaps the most natural connection between group theory and graph theory lies in finding the automorphism group of a given graph. However, by studying the opposite connection, that is, find...

We study the quantum sphere Cq [S] as a quantum Riemannian manifold in the quantum frame bundle approach. We exhibit its 2-dimensional cotangent bundle as a direct sum Ω ⊕ Ω in a double complex. We find the natural metric, volume form, Hodge * operator, Laplace and Maxwell operators. We show that the q-monopole as spin connection induces a natural Levi-Civita type connection and find its Ricci ...

Let k be an algebraically closed field of characteristic 0, and let A = k[x, y]/(f) be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M without free summands, there exists a natural graded integrable connection, i.e. a graded A-linear homomorphism ∇ : Derk(A) → Endk(M) that satisfy the derivation property and preserves the Lie product. In particular, a torsio...

Parabolic geometries may be considered as curved analogues of the homogeneous spaces G/P where G is a semisimple Lie group and P ⊂ G a parabolic subgroup. Conformal geometries and CR geometries are examples of such structures. We present a uniform description of a calculus, called tractor calculus, based on natural bundles with canonical linear connections for all parabolic geometries. It is sh...

We consider a vector bundle E →M and the principal bundle PE of frames of E. We determine all natural transformations of the connection bundle of the first order principal prolongation of principal bundle PE into itself. Unless otherwise specified, we use the terminology and notation from the book [7]. All manifolds and maps are assumed to be infinitely differentiable. In the monograph [7], the...

This paper examines the problematization of cultural issues related tothe dual spacization of life. The emergence of the second space of lifeover the first place of life combining local and translocal, national andtransnational capacities and challenges. We discuss the capacities andopportunities occurring through the instant communication industrywhich made the spontaneous connection between a...

the tele-connection patterns are the major constituents of climate at global and regional scale(s). the karoon basin is of a vital stance in providing natural water supply and hydroelectric; this basin is facing major fluctuations in rainfall regime. identifying the effect of tele-connection on great karoon basin rainfall regime is the subject of this study. to accomplish this objective the sea...