13 citations · 85 across the 25 of their papers we have counts for
26 papers
Calibrations close to -twistor space
Rui Albuquerque
We study natural structures of the kind of existing on the unit tangent sphere bundle of any oriented Riemannian 4-manifold . Based on the Harv…
The mirror map and other natural tangent tensors
R. Albuquerque
We review the intrinsic geometry of the tangent bundle of a differentiable manifold , aside from any non-natural structures. We recall the properties of the mirror map $B\in\mat…
On the volume of a unit vector field in 3 dimensions via calibrations
Rui Albuquerque
We give a new proof of the well-known result that the minimal volume vector fields on are the Hopf vector fields. Such proof relies again on calibration theory, a…
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 , that is, the arbitrary radius 2-sphere with two antipodal…
New Hsiung-Minkowski identities
R. Albuquerque
We find the first three most general Minkowski or Hsiung-Minkowski identities relating the total mean curvatures , of degrees , of a closed hypersurface immersed…
The Euler characteristic of hypersurfaces in space forms and applications to isoparametric hypersurfaces
R. Albuquerque
We revisit Allendoerfer-Weil's formula for the Euler characteristic of embedded hypersurfaces in constant sectional curvature manifolds, first taking some time to re-prove it while…
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…
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,…
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…
An invariant Kähler metric on the tangent disk bundle of a space-form
Rui Albuquerque
We find a family of Kähler metrics invariantly defined on the radius tangent disk bundle of any given real space-form or any of its quotients by di…
Natural SU(2)-structures on tangent sphere bundles
R. Albuquerque
We define and study natural -structures, in the sense of Conti-Salamon, on the total space of the tangent sphere bundle of any given oriented Riemannian 3-…
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…
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 , ov…
Self-duality and associated parallel or cocalibrated structures
Rui Albuquerque
We find a remarkable family of structures defined on certain principal -bundles associated with any given oriented Riemannia…
A fundamental differential system of Riemannian geometry
Rui Albuquerque
We discover a fundamental exterior differential system of Riemannian geometry; indeed, an intrinsic and invariant global system of differential forms of degree associated to an…
Curvatures of weighted metrics on tangent sphere bundles
Rui Albuquerque
We determine the curvature equations of natural metrics on tangent bundles and radius r tangent sphere bundles S_rM of a Riemannian manifold M. A family of positive scalar curvatur…
On invariants of almost symplectic connections
Rui Albuquerque, Roger Picken
We study the irreducible decomposition under Sp(2n, R) of the space of torsion tensors of almost symplectic connections. Then a description of all symplectic quadratic invariants o…
Variations of gwistor space
Rui Albuquerque
We study natural variations of the G2 structure σ_0 \in Λ^3_+ existing on the unit tangent sphere bundle SM of any oriented Riemannian 4-manifold M. We find a circle of structures…
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…
Weighted metrics on tangent sphere bundles
Rui Albuquerque
Natural metric structures on the tangent bundle and tangent sphere bundles of a Riemannian manifold with radius function enclose many important unsolved problems. Ad…
Homotheties and topology of tangent sphere bundles
Rui Albuquerque
We prove a Theorem on homotheties between two given tangent sphere bundles of a Riemannian manifold of , assuming different variable radius functions a…
Isometries and curvatures of tangent sphere bundles
Rui Albuquerque
Natural metric structures on tangent bundles and tangent sphere bundles enclose many important problems, from the topology of the base to the determination of their holonomy. We ma…
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…
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…