Centro de Investigação em Matemática e Aplicações

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20012022

most citedOn polynomials with given Hilbert function and applications

15 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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17 papers · 1 filter

math.DG2021★ 1 cited

Vector fields with big and small volume on the 2-sphere

Rui Albuquerque

We consider the problem of minimal volume vector fields on a given Riemann surface, specialising on the case of $M^{⋆}$ , that is, the arbitrary radius 2-sphere with two antipodal…

math.DG2021

The volume of a unit vector field in 2 dimensions via calibrations

Rui Albuquerque

We use the theory of calibrations to write the equation of a minimal volume vector field on a given Riemann surface.

math.DG2021

New Hsiung-Minkowski identities

R. Albuquerque

We find the first three most general Minkowski or Hsiung-Minkowski identities relating the total mean curvatures $H_{i}$ , of degrees $i = 1, 2, 3$ , of a closed hypersurface $N$ immersed…

math.DG2018★ 3 cited

Minkowski identities for hypersurfaces in constant sectional curvature manifolds

R. Albuquerque

We 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 cur…

math.DG2018★ 6 cited

Notes on the Sasaki metric

Rui Albuquerque

We 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,…

math.DG2016★ 4 cited

The ciconia metric on the tangent bundle of an almost-Hermitian manifold

Rui Albuquerque

We 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 ex…

math.DG2016★ 1 cited

Natural SU(2)-structures on tangent sphere bundles

R. Albuquerque

We 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-…

math.DG2015★ 4 cited

A fundamental differential system of 3-dimensional Riemannian geometry

Rui Albuquerque

We briefly recall a fundamental exterior differential system introduced by the author and then apply it to the case of three dimensions. Here we find new global tensors and intrins…

math.DG2014★ 8 cited

On vector bundle manifolds with spherically symmetric metrics

Rui Albuquerque

We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle $E \to M$ , ov…

math.DG2014

Self-duality and associated parallel or cocalibrated $G_{2}$ structures

Rui Albuquerque

We find a remarkable family of $G_{2}$ structures defined on certain principal $SO (3)$ -bundles $P_{\pm} ⟶ M$ associated with any given oriented Riemannia…

math.DG2011★ 4 cited

On the characteristic connection of gwistor space

Rui Albuquerque

We give a brief presentation of gwistor space, which is a new concept from G_2 geometry. Then we compute the characteristic torsion T^c of the gwistor space of an oriented Riemanni…

math.DG2010★ 7 cited

Weighted metrics on tangent sphere bundles

Rui Albuquerque

Natural metric structures on the tangent bundle and tangent sphere bundles $S_{r} M$ of a Riemannian manifold $M$ with radius function $r$ enclose many important unsolved problems. Ad…

math.DG2010★ 10 cited

Homotheties and topology of tangent sphere bundles

Rui Albuquerque

We prove a Theorem on homotheties between two given tangent sphere bundles $S_{r} M$ of a Riemannian manifold $M, g$ of $dim \geq 3$ , assuming different variable radius functions $r$ a…

math.DG2008★ 13 cited

On the G_2 bundle of a Riemannian 4-manifold

Rui Albuquerque

We study the natural G_2 structure on the unit tangent sphere bundle SM of any given orientable Riemannian 4-manifold M, as it was discovered in \cite{AlbSal}. A name is proposed f…

math.DG2007

Remarks on symplectic twistor spaces

Rui Albuquerque

We consider some classical fibre bundles furnished with almost complex structures of twistor type, deduce their integrability in some cases and study \textit{self-holomorphic} sect…

math.DG2007★ 2 cited

Hermitian and quaternionic Hermitian structures on tangent bundles

Rui Albuquerque

We review the theory of quaternionic Kahler and hyperkahler structures. Then we consider the tangent bundle of a Riemannian manifold M with a metric connection D (with torsion) and…

math.DG2006★ 5 cited

The G_2 sphere over a 4-manifold

R. Albuquerque, I. M. C. Salavessa

We present a construction of a canonical G_2 structure on the unit sphere tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such structure is never geometric or 1…

Vector fields with big and small volume on the 2-sphere

The volume of a unit vector field in 2 dimensions via calibrations

New Hsiung-Minkowski identities

Minkowski identities for hypersurfaces in constant sectional curvature manifolds

Notes on the Sasaki metric

The ciconia metric on the tangent bundle of an almost-Hermitian manifold

Natural SU(2)-structures on tangent sphere bundles

A fundamental differential system of 3-dimensional Riemannian geometry

On vector bundle manifolds with spherically symmetric metrics

Self-duality and associated parallel or cocalibrated G2​ structures

On the characteristic connection of gwistor space

Weighted metrics on tangent sphere bundles

Homotheties and topology of tangent sphere bundles

On the G_2 bundle of a Riemannian 4-manifold

Remarks on symplectic twistor spaces

Hermitian and quaternionic Hermitian structures on tangent bundles

The G_2 sphere over a 4-manifold

Self-duality and associated parallel or cocalibrated $G_{2}$ structures