Weyl-parallel forms, conformal products and Einstein-Weyl manifolds

Motivated by the study of Weyl structures on conformal manifolds admitting parallel weightless forms, we define the notion of conformal product of conformal structures and study its basic properties. We obtain a classification of Weyl manifolds carrying parallel forms, and we use it to investigate the holonomy of the adapted Weyl connection on conformal products. As an application we describe a new class of Einstein-Weyl manifolds of dimension 4.Comment: 24 page

On the irreducibility of locally metric connections

A locally metric connection on a smooth manifold $M$ is a torsion-free connection $D$ on $TM$ with compact restricted holonomy group $\mathrm{Hol}_0(D)$. If the holonomy representation of such a connection is irreducible, then $D$ preserves a conformal structure on $M$. Under some natural geometric assumption on the life-time of incomplete geodesics, we prove that conversely, a locally metric connection $D$ preserving a conformal structure on a compact manifold $M$ has irreducible holonomy representation, unless $\mathrm{Hol}_0(D)=0$ or $D$ is the Levi-Civita connection of a Riemannian metric on $M$. This result generalizes Gallot's theorem on the irreducibility of Riemannian cones to a much wider class of connections. As an application, we give the geometric description of compact conformal manifolds carrying a tame closed Weyl connection with non-generic holonomy.Comment: 26 pages, 4 figure

Symmetries of Contact Metric Manifolds

We study the Lie algebra of infinitesimal isometries on compact Sasakian and K--contact manifolds. On a Sasakian manifold which is not a space form or 3--Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian structure. For a manifold with K--contact structure, we prove that there exists a Killing vector field of constant length which is not an infinitesimal automorphism of the structure if and only if the manifold is obtained from the Konishi bundle of a compact pseudo--Riemannian quaternion--Kaehler manifold after changing the sign of the metric on a maximal negative distribution. We also prove that non--regular Sasakian manifolds are not homogeneous and construct examples with cohomogeneity one. Using these results we obtain in the last section the classification of all homogeneous Sasakian manifolds.Comment: 14 pages, LaTeX2e, some comments and references adde

Macro Variables Impact on Credit Risk and Influence in Banking Capital and Job Cuts in Romania

The scope of the research paper is to capture the connection between the representative macro-economic variables, gross domestic product, gross salary income, exchange rate EUR/RON, active interest rate and unemployment rate, respectively the variables which quantify the credit risk, non-performing loans rate and credit risk rate. For the quantitative analysis we used the VAR econometric models, the study being completed with a qualitative analysis which observes the influence in the credit institutions capital and the available jobs in the financial-banking system. The results obtained showed a considerable influence of the exchange rate, gross salary income and interest rate on the credit risk rate, while the non-performing loans rate was mostly influenced by the interest rate and gross salary income. The qualitative analysis exposed that at global level the losses registered in the banking sector were about 1.2 trillion USD, while the new capital raised was about 1 trillion USD and almost 390 thousand job cuts. In the Romanian banking sector, the study illustrates cumulated losses of 13.3 billion lei, compensated by an increase in capital at about 21 billion lei and restructuring of about 15 thousand jobs. The results obtained have both practical applicability, but also in the economic policies, clearly exposing the effects of the credit risk through the deterioration of the macro-economic environment. The information presented through the empirical analysis can be used by the researches, supervision and regulatory authorities or by the credit institutions in stress testing, forecasts or resolution decisions

CHANGING LEARNING ENVIRONMENT THROUGH TECHNOLOGY

Evolution of E-learning phenomenon exceeded all expectations in recent years.As a result of development of IT&C technologies and, on the other hand, due to support decision-makers at European level, the assimilation of virtual learning platforms in schools and universities hasbecome a normal phenomenon.The E-learning 2.0 concept seeks to revolutionize traditional learning methods and requires majorchanges in the perception of the educational process of teaching and learning.This article tries to create an overview of the main development directions and emphasizes the impactthat computer-assisted instruction technologies have on teaching and learning methods, with a directconnection to distance learning and blended learning concepts. Also, we have tried to open aperspective on the concept of e-Assessment and related technologiese-learning 2.0, computer based training, e-assessment, blended learning, distance learning

Holonomy of tame Weyl Structures

29 pages, 5 figuresA Weyl structure on a compact conformal manifold is not complete in general. If, however, the life-time of incomplete geodesics can be controlled on compact subsets of the tangent bundle, the Weyl connection is called tame. We prove that every closed, non-exact, tame Weyl structure on a compact conformal manifold is either flat, or has irreducible holonomy, generalizing a classical statement for Riemannian cone metrics by S. Gallot

Weyl-parallel Forms and conformal Products

18 pagesMotivated by the study of Weyl structures on conformal manifolds admitting parallel weightless forms, we define the notion of conformal product of conformal structures and study its basic properties. We obtain a classification of Weyl manifolds carrying parallel forms, and we use it to describe in further detail the holonomy of the adapted Weyl connection on conformal products