Quaternionic K\"ahler metrics associated with special K\"ahler manifolds

We give an explicit formula for the quaternionic K\"ahler metrics obtained by the HK/QK correspondence. As an application, we give a new proof of the fact that the Ferrara-Sabharwal metric as well as its one-loop deformation is quaternionic K\"ahler. A similar explicit formula is given for the analogous (K/K) correspondence between K\"ahler manifolds endowed with a Hamiltonian Killing vector field. As an example, we apply this formula in the case of an arbitrary conical K\"ahler manifold.Comment: 30 pages, appendix extended, final version published in JG

Flows on quaternionic-Kaehler and very special real manifolds

BPS solutions of 5-dimensional supergravity correspond to certain gradient flows on the product M x N of a quaternionic-Kaehler manifold M of negative scalar curvature and a very special real manifold N of dimension n >=0. Such gradient flows are generated by the `energy function' f = P^2, where P is a (bundle-valued) moment map associated to n+1 Killing vector fields on M. We calculate the Hessian of f at critical points and derive some properties of its spectrum for general quaternionic-Kaehler manifolds. For the homogeneous quaternionic-Kaehler manifolds we prove more specific results depending on the structure of the isotropy group. For example, we show that there always exists a Killing vector field vanishing at a point p in M such that the Hessian of f at p has split signature. This generalizes results obtained recently for the complex hyperbolic plane (universal hypermultiplet) in the context of 5-dimensional supergravity. For symmetric quaternionic-Kaehler manifolds we show the existence of non-degenerate local extrema of f, for appropriate Killing vector fields. On the other hand, for the non-symmetric homogeneous quaternionic-Kaehler manifolds we find degenerate local minima.Comment: 22 page

El sentido literal y el sentido espiritual de la Sagrada Escritura

SUMARIO: 1. LA HERMENÉUTICA EN EL SENO DE LA BIBLIA. 1.1. Jesucristo y la interpretación de la Escritura. 1.2. El Nuevo Testamento. 2. LOS SENTIDOS HASTA LA SÍNTESIS TOMISTA. 2.1. La exégesis antigua. 2.2. Santo Tomás y los sentidos bíblicos. 2.3. La articulación de la solución tomista. 3. EL CAMBIO DE PARADIGMA. LA REFORMA Y EL RACIONALISMO. 4. LOS SENTIDOS BÍBLICOS EN LA EXÉGESIS CATÓLICA DEL ÚLTIMO SIGLO. 4.1. Las encíclicas bíblicas. 4.2. Dei Verbum. 4.3. El sentido de la Escritura en la investigación desde «Divino Afflante Spiritu». 4.4. El documento de la Pontificia Comisión Bíblica «La interpretación de la Biblia en la Iglesia». 5. UNA TEORÍA DEL SENTIDO Y DE LOS CONTEXTOS DE INTERPRETACIÓN DE LOS TEXTOS. 5.1. Aplicación a la Sagrada Escritura en la Iglesia. 5.2. Las posiciones de la exégesis a la luz de estas consideraciones. 6. CONCLUSIÓN