35 documents found, page 1 of 4
A contribution to the EU’s economic governance review : the importance of stron...
Albuquerque, Rui; Marques, Luís Brandão; Costa, CarlosLusíada. Economia & Empresa. ISSN 1645-6750. S. 2, n. 38 (2025).; The EU’s 2024 fiscal governance reform is a step forward, but it misses an opportunity to empower National Fiscal Councils (NFCs). Stronger NFCs could enhance fiscal discipline, accountability, and public engagement. NFCs with increased independence, funding, and authority can improve the quality of fiscal forecasts, challenge unsustainable polic...
An invariant Kähler metric on the tangent disk bundle of a space-form
Albuquerque, RuiWe find a family of Kähler metrics invariantly defined on the radius r0 > 0 tangent disk bundle TM_r0 of any given real space-form M or any of its quotients by discrete groups of isometries. Such metrics are complete in the non-negative curvature case and non-complete in the negative curvature case. If dim M = 2 and M has constant sectional curvature K nonvanishing, then the Kähler manifolds TM_r0 have holonomy...
Natural SU(2)-structures on tangent sphere bundles
Albuquerque, RuiWe define and study natural SU(2)-structures, in the sense of Conti–Salamon, on the total space S of the tangent sphere bundle of any given oriented Riemannian 3-manifold M. We recur to a fundamental exterior differential system of Riemannian geometry. Essentially, two types of structures arise: the contact-hypo and the non-contact and, for each, we study the conditions for being hypo, nearly-hypo or double-hyp...
The Euler characteristic of hypersurfaces in space forms and its application to...
Albuquerque, RuiWe revisit the Allendoerfer–Weil formula for the Euler characteristic of embedded hypersurfaces in constant sectional curvature manifolds, taking time to re-prove it while demonstrating techniques of ([http://hdl.handle.net/10174/26893]) and then applying it to gain new understanding of isoparametric hypersurfaces.
New Hsiung-Minkowski identities
Albuquerque, RuiWe find the first three most general Minkowski or Hsiung–Minkowski identities relating the total mean curvatures , of degrees =0,1,2,3, of a closed hypersurface N immersed in a given orientable Riemannian manifold M endowed with any given vector field P. Then we specialize the three identities to the case when P is a position vector field. We further obtain that the classical Minkowski identity is natural to al...
The ciconia metric on the tangent bundle of an almost-Hermitian manifold
Albuquerque, RuiWe find a new class of invariant metrics existing on the tangent bundle of any given almost Hermitian manifold. We focus here on the case of Riemannian surfaces, which yield new examples of Kählerian Ricci-flat manifolds in four real dimensions.
A fundamental differential system of Riemannian geometry
Albuquerque, RuiWe discover a fundamental exterior differential system of Riemannian geometry; indeed, an intrinsic and invariant global system of differential forms of degree n associated to any given oriented Riemannian manifold M of dimension n + 1. The framework is that of the tangent sphere bundle of M. We generalise to a Riemannian setting some results from the theory of hypersurfaces in flat Euclidean space. We give new...
Notes on the Sasaki metric
Albuquerque, RuiWe survey on the geometry of the tangent bundle of a Riemannian manifold, endowed with the classical metric established by S. Sasaki 60 years ago. Following the results of Sasaki, we try to write and deduce them by different means. Questions of vector fields, mainly those arising from the base, are related as invariants of the classical metric, contact and Hermitian structures. Attention is given to the natural...
Self-duality and associated parallel or cocalibrated G2 structures
Albuquerque, RuiWe find a remarkable family of G2 structures defined on certain principal SO(3)-bundles P± → M associated with any given oriented Riemannian 4-manifold M. Such structures are always cocalibrated. The study starts with a recast of the Singer–Thorpe equations of 4-dimensional geometry. These are applied to the Bryant–Salamon construction of complete G2-holonomy metrics on the vector bundle of self- or anti-self-d...
Minkowski identities for hypersurfaces in constant sectional curvature manifolds
Albuquerque, RuiWe give a new proof of the generalized Minkowski identities relating the higher degree mean curvatures of orientable closed hypersurfaces immersed in a given constant sectional curvature manifold. Our methods rely on a fundamental differential system of Riemannian geometry introduced by the author. We develop the notion of position vector field, which lies at the core of the Minkowski identities.