Geometric and Extensor Algebras and the Differential Geometry of Arbitrary Manifolds

We give in this paper which is the third in a series of four a theory of covariant derivatives of representatives of multivector and extensor fields on an arbitrary open set U of M, based on the geometric and extensor calculus on an arbitrary smooth manifold M. This is done by introducing the notion of a connection extensor field gamma defining a parallelism structure on U, which represents in a well defined way the action on U of the restriction there of some given connection del defined on M. Also we give a novel and intrinsic presentation (i.e., one that does not depend on a chosen orthonormal moving frame) of the torsion and curvature fields of Cartan's theory. Two kinds of Cartan's connection operator fields are identified, and both appear in the intrinsic Cartan's structure equations satisfied by the Cartan's torsion and curvature extensor fields. We introduce moreover a metrical extensor g in U corresponding to the restriction there of given metric tensor \slg defined on M and also introduce the concept a geometric structure (U,gamma,g) for U and study metric compatibility of covariant derivatives induced by the connection extensor gamma. This permits the presentation of the concept of gauge (deformed) derivatives which satisfy noticeable properties useful in differential geometry and geometrical theories of the gravitational field. Several derivatives operators in metric and geometrical structures, like ordinary and covariant Hodge coderivatives and some duality identities are exhibit.Comment: This paper is an improved version of material contained in math.DG/0501560, math.DG/0501561, math.DG/050200

La gestión de los comunes en México : hacia un modelo de análisis de los ejidos

En este artículo se presentan algunos resultados y cuestionamientos que surgieron a través de la investigación "Las instituciones locales de acción colectiva en la gestión de los comunes en México: el Ejido tras las reformas agrarias de 1992" realizado en el marco del Máster en Investigación etnográfica, teoría antropológica y relaciones interculturales de la Universidad Autónoma de Barcelona (UAB) 2010- 2011. Como objetivo principal de esta investigación se analizaron las consecuencias de las reformas agrarias emprendidas desde 1992 en las instituciones locales de acción colectiva de los ejidos. El ejido es la figura jurídica más representativa de la propiedad colectiva en México. Por otra parte, nos centramos en el programa PROCEDE (Programa de Certificación de Derechos Ejidales y Titulación de Solares Urbanos) como la principal herramienta de la Ley Agraria de 1992 y la reforma del artículo 27 Constitucional. Asimismo, en este artículo se aporta la propuesta metodológica para el análisis de casos (ejidos) en el proceso de estas reformas legislativas.This article presents some results and questions that emerged through the research "Local institutions for collective action in managing common in Mexico: the Ejido after the land reform of 1992" made for the Master in Ethnographic Research, Anthropological Theory and Intercultural Relations at the Autonomous University of Barcelona(UAB) 2010 - 2011. As the main goal of this research I analyzed the impact of land reforms undertaken since 1992 in local institutions for collective action of the ejidos. The ejido is the main legal form of common property in Mexico. Moreover, we focus on the PROCEDE program (Program of Certification of Ejido Rights and Titling of Urban Patios) as the main tool of the Agrarian Law of 1992 and the reform of Article 27 of the Constitution. Also, this article provides a methodological proposal for analyzing ejidos case studies in the context of these legislative reforms

Paloma Fernández Pérez (2012), La última globalización y el renacer de los grandes negocios familiares en el mundo, Universidad de los Andes, Bogotá, 95 pp. Este

Este libro recog

Geometric Algebras and Extensors

This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of geometrical theories of the gravitational field. In this first paper we introduce the key algebraic tools for the development of our program, namely the euclidean geometrical algebra of multivectors Cl(V,G_{E}) and the theory of its deformations leading to metric geometric algebras Cl(V,G) and some special types of extensors. Those tools permit obtaining, the remarkable golden formula relating calculations in Cl(V,G) with easier ones in Cl(V,G_{E}) (e.g., a noticeable relation between the Hodge star operators associated to G and G_{E}). Several useful examples are worked in details fo the purpose of transmitting the "tricks of the trade".Comment: This paper (to appear in Int. J. Geom. Meth. Mod. Phys. 4 (6) 2007) is an improved version of material appearing in math.DG/0501556, math.DG/0501557, math.DG/050155