The Riemannian manifold of all Riemannian metrics

The space of all Riemannian metrics on a smooth second countable finite dimensional manifold is itself a smooth manifold modeled on the space of symmetric (0,2)-tensor fields with compact support. It carries a canonical Riemannian metric which is invariant under the action of the diffeomorphism group. We determine its geodesics, exponential mapping, curvature, and Jacobi fields in a very explicit manner

Pseudoriemannian metrics on spaces of bilinear structures

The space of all non degenerate bilinear structures on a manifold $M$ carries a one parameter family of pseudo Riemannian metrics. We determine the geodesic equation, covariant derivative, curvature, and we solve the geodesic equation explicitly. Each space of pseudo Riemannian metrics with fixed signature is a geodesically closed submanifold. The space of non degenerate 2-forms is also a geodesically closed submanifold. Then we show that, if we fix a distribution on $M$, the space of all Riemannia metrics splits as the product of three spaces which are everywhere mutually orthogonal, for the usual metric. We investigate this situation in detail

The temporal duration of public posts in republican Rome: a cause for reflection

La duración limitada de las magistraturas en la Roma republicana y su posterior decadencia con la prorrogatio imperii, nos hace reflexionar sobre la relevancia de la temporalidad de los cargos públicos como garantía de un sistema democrático. Utilizando el ejemplo romano, comparamos lo que sucede desde la entrada en vigor de nuestra Constitución de 1978 hasta hoy, y observamos con preocupación, como la durabilidad en los mandatos de los principales órganos constitucionales se está relajando, sin que ni siquiera existan los motivos que en Roma justificaron la prorrogatio imperii.The limited duration of magistratures in Republican Rome and its subsequent decline due to prorogatio imperii leads us to reflect on the relevance of the temporal duration of public posts as a guarantee of a democratic system. Using the Roman example, we compare events since the entry into force of the Spanish Constitution of 1978 up until today, and we note with concern, how durability in the mandates of the principal constitutional organs is becoming more relaxed, without the motives even existing that justified prorogatio imperii in Rome

La Unión Europea, las comunicaciones electrónicas y los bienes digitales

Se estudia el cambio en la regulación de las comunicaciones electrónicas en la Unión Europea (UE) con la aprobación de un nuevo paquete de directivas en la primavera de 2002 y las implicaciones para otros niveles de gobierno e instituciones. Se trata de determinar si este cambio en las políticas públicas va a plasmarse en un nuevo contexto institucional más favorable para la competencia, y para la cooperación entre actores políticos de diferentes niveles de gobierno y sociales, a tenor de la trasposición de las directivas a la normativa interna de los países. Este objetivo tiene un ámbito de aplicación más general, por cuanto que las nuevas políticas públicas se estudian desde la óptica de la regulación de los bienes digitales (secuencias de dígitos binarias ceros y unos-, que afectan a la utilidad o beneficio de un individuo en una economía dada). Realizar el estudio desde la óptica de la regulación de los bienes digitales implica que algunas conclusiones pueden ser extrapolables a bienes digitales distintos de los electrónicos (ie. Productos biotecnológicos).Implications of the new framework for the regulation of electronic communications in the European Union are analysed for the different levels of government and institutions. The ultimate goal is to determine whether the aforementioned change facilitates a new institutional context, more favourable to competition and cooperation of political and social actors involved. Conclusions have a broader scope of application, since the new policies set in place are studied having in mind the central place that digital goods (sequences of binary digits, Os and Is, that affects the utility of or payoff to some individual in the economy) have in the New Economy —an economy where digital goods figure prominently in determining aggregate economic outcomes (innovation, production, consumption) Some reflections may thus be applied to other related cases involving other digital goods, such as biotechnological products

Public participation in China and the West

This work shows differences in public participation in China and Western countries, conceptually and empirically. To do so, the different philosophical and public administration traditions are outlined. Main contributions are tables and dashboards to allow general comparisons and to differentiate contexts in both political settings, besides being useful for other settings. The tables included are: 1) Main features of context in China, 2) Deliberative democracy, 3) Main features of context in the west, 4) The Gil Dashboard helping to outline the endogenous foundations for change both in China and the West