Contact pairs and locally conformally symplectic structures

We discuss a correspondence between certain contact pairs on the one hand, and certain locally conformally symplectic forms on the other. In particular, we characterize these structures through suspensions of contactomorphisms. If the contact pair is endowed with a normal metric, then the corresponding lcs form is locally conformally Kaehler, and, in fact, Vaisman. This leads to classification results for normal metric contact pairs. In complex dimension two we obtain a new proof of Belgun's classification of Vaisman manifolds under the additional assumption that the Kodaira dimension is non-negative. We also produce many examples of manifolds admitting locally conformally symplectic structures but no locally conformally Kaehler ones.Comment: 13 pages; corrected two misprints; to appear in Contemporary Mathematic

The NRU and the Evolution of Regional Disparities in Spanish Unemployment

On both theoretical and empirical grounds, this paper provides evidence that refutes the natural rate of unemployment (NRU) hypothesis as an explanation of the evolution of regional disparities in the unemployment rate. We first present our analytical framework, which follows the chain reaction theory (CRT) of unemployment and argues that (i) a system of interactive labour market equations, rather than a single-equation unemployment rate model, is better equipped to accommodate unemployment dynamics, and (ii) due to the interplay of frictions and growth in labour markets, the NRU ceases to be an attractor of the unemployment rate time path. We then provide evidence that the Spanish economy is characterised by large and persistent disparities in the regional unemployment rates. Through standard kernel density tecnhiques, we demonstrate the existence of marked differences between two groups of high and low unemployment regions that remain stable in their composition through time. Finally, we review our empirical labour market model for each group of regions and evaluate the corresponding natural rates. Our findings confirm that the evolution of regional disparities cannot be attributed to disparities in the natural rates, given that these, although different, do not act as an attractor of unemployment. Thus, the NRUs offer little help in the formulation of labour market policies.regional unemployment, disparities, kernel, natural rate, frictional growth

Labour Market Flexibility and Regional Unemployment Rate Dynamics: Spain 1980-1995

This paper aims to shed light in the dynamics of Spanish regional unemployment rates and determine the driving forces of their disparities. The Spanish economy has one of the highest unemployment rates in the EU and is characterised by severe regional disparities. We apply the chain reaction theory of unemployment according to which the evolution of unemployment is driven by the interplay of lagged adjustment processes and the spillover effects within the labour market system. Our model includes nationwide as well as region-specific variables, and takes into account the limited labour and firm mobility in Spain. We show that the degree of labour market flexibility differs between high and low unemployment regions, and find that investment has a major influence on the unemployment trajectory. In addition, we find that in bad times high unemployment regions are hit more severely than low unemployment regions, while in good times high unemployment regions do not benefit as much as low unemployment regions.Regional disparities, Unemployment, Spillover effects, Labour market lagged adjustment processes

The geometry of symplectic pairs

We study the geometry of manifolds carrying symplectic pairs consisting of two closed 2-forms of constant ranks, whose kernel foliations are complementary. Using a variation of the construction of Boothby and Wang we build contact-symplectic and contact pairs from symplectic pairs.Comment: to appear in Transactions of the American Mathematical Societ

Wage flexibility and local labour markets: homogeneity of the wage curve in Spain

In this paper we analyse wage flexibility in Spain and its regional differences, departing from the estimation of wage curves. Specifically, and using as the main data source the Wage Structure Survey, we proceed to estimate for each Spanish region a wage equation, which explains observed wage received by workers to a group of personal and job characteristics, as well as the unemployment rate. This analysis allows to test hypothesis concerning the possible changes that may have occurred in each region in the degree of wage flexibility between the two years considered in the Survey. Also, we test the existence of regional differences in the degree of wage flexibility, which may have an important influence in the evolution of regional unemployment, given its impact on the ability of the local labour market to absorb negative shocks. The paper also allows to analyse the variability of the wage flexibility estimation with respect to the dependent variable, which could explain opposite results in the existing literature

Minimality of invariant submanifolds in Metric Contact Pair Geometry

We study invariant submanifolds of manifolds endowed with a normal or complex metric contact pair with decomposable endomorphism field $\phi$. For the normal case, we prove that a $\phi$-invariant submanifold tangent to a Reeb vector field and orthogonal to the other one is minimal. For a $\phi$-invariant submanifold $N$ everywhere transverse to both the Reeb vector fields but not orthogonal to them, we prove that it is minimal if and only if the angle between the tangential component $\xi$ (with respect to $N$) of a Reeb vector field and the Reeb vector field itself is constant along the integral curves of $\xi$. For the complex case (when just one of the two natural almost complex structures is supposed to be integrable), we prove that a complex submanifold is minimal if and only if it is tangent to both the Reeb vector fields.Comment: To appear in "Ann. Mat. Pura Appl. (4)", March 201