For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose of this construction is to realise the normal conformal tractor holonomy as affine holonomy of such a connection. We give an example of an ambient connectio...

In this paper we study two different topics. The first topic is the applications of the geometric quantization scheme of Witten introduced in [2] and [16] to the problem of the quantum background independence in string theory. The second topic is the introduction of a Z structure on the tangent space of the moduli space of polarized CY threefolds M(M). Based on the existence of a Z structure on...

We improve Chen-Ricci inequalities for a Lagrangian submanifold Mn of dimension n (n 2) in a 2n -dimensional complex space form M̃2n(4c) of constant holomorphic sectional curvature 4c with a semi-symmetric metric connection and a Legendrian submanifold Mn in a Sasakian space form M̃2n+1(c) of constant φ -sectional curvature c with a semi-symmetric metric connection, respectively.

For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose of this construction is to realise the normal conformal tractor holonomy as affine holonomy of such a connection. We give an example of an ambient connectio...

We prove that Wigner functions contain a symplectic connection. The latter covariantises the symplectic exterior derivative on phase space. We analyse the role played by this connection and introduce the notion of local symplectic covariance of quantum–mechanical states. This latter symmetry is at work in the Schroedinger equation on phase space.

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...

General properties of Abelian connection in Fedosov deformation quantization are investigated. Criteria of being a finite series for an Abelian connection are presented. Conditions for different symplectic connections to generate the same correction to the Abelian connection are given. A proof that in 2–dimensional case the Abelian connection is an ifinite series is done. A class of symplectic ...