42 research outputs found
Deformations des feuilletages transversalement holomorphes a type differentiable fixe
Let F be a transversely holomorphic foliation on a compact manifold. We show the existence of a versal space for those deformations of F which keep fixed its differentiable type if F is hermitian or if F has complex codimension one and admits a transverse projectable connection. We also prove the existence of a versal space of deformations for the complex structures on a Lie group invariant by a cocompact subgroup
Modified differentials and basic cohomology for Riemannian foliations
We define a new version of the exterior derivative on the basic forms of a
Riemannian foliation to obtain a new form of basic cohomology that satisfies
Poincar\'e duality in the transversally orientable case. We use this twisted
basic cohomology to show relationships between curvature, tautness, and
vanishing of the basic Euler characteristic and basic signature.Comment: 20 pages, references added, minor corrections mad
On Sasaki-Einstein manifolds in dimension five
We prove the existence of Sasaki-Einstein metrics on certain simply connected
5-manifolds where until now existence was unknown. All of these manifolds have
non-trivial torsion classes. On several of these we show that there are a
countable infinity of deformation classes of Sasaki-Einstein structures.Comment: 18 pages, Exposition was expanded and a reference adde
Randomizing world trade. II. A weighted network analysis
Based on the misleading expectation that weighted network properties always
offer a more complete description than purely topological ones, current
economic models of the International Trade Network (ITN) generally aim at
explaining local weighted properties, not local binary ones. Here we complement
our analysis of the binary projections of the ITN by considering its weighted
representations. We show that, unlike the binary case, all possible weighted
representations of the ITN (directed/undirected, aggregated/disaggregated)
cannot be traced back to local country-specific properties, which are therefore
of limited informativeness. Our two papers show that traditional macroeconomic
approaches systematically fail to capture the key properties of the ITN. In the
binary case, they do not focus on the degree sequence and hence cannot
characterize or replicate higher-order properties. In the weighted case, they
generally focus on the strength sequence, but the knowledge of the latter is
not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243
[physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011
Energy properness and Sasakian-Einstein metrics
In this paper, we show that the existence of Sasakian-Einstein metrics is
closely related to the properness of corresponding energy functionals. Under
the condition that admitting no nontrivial Hamiltonian holomorphic vector
field, we prove that the existence of Sasakian-Einstein metric implies a
Moser-Trudinger type inequality. At the end of this paper, we also obtain a
Miyaoka-Yau type inequality in Sasakian geometry.Comment: 27 page
The odd side of torsion geometry
We introduce and study a notion of `Sasaki with torsion structure' (ST) as an
odd-dimensional analogue of K\"ahler with torsion geometry (KT). These are
normal almost contact metric manifolds that admit a unique compatible
connection with 3-form torsion. Any odd-dimensional compact Lie group is shown
to admit such a structure; in this case the structure is left-invariant and has
closed torsion form.
We illustrate the relation between ST structures and other generalizations of
Sasaki geometry, and explain how some standard constructions in Sasaki geometry
can be adapted to this setting. In particular, we relate the ST structure to a
KT structure on the space of leaves, and show that both the cylinder and the
cone over an ST manifold are KT, although only the cylinder behaves well with
respect to closedness of the torsion form. Finally, we introduce a notion of
`G-moment map'. We provide criteria based on equivariant cohomology ensuring
the existence of these maps, and then apply them as a tool for reducing ST
structures.Comment: 34 pages; v2: added a small generalization (Proposition 3.6) of the
cone construction; two references added. To appear on Ann. Mat. Pura App
Fonctionnelles invariantes et courants basiques
Dans ce travail: (1) on caractérise l'espace des fonctionnelles invariantes par un groupe compact G opérant linéairement et continûment sur un espace vectoriel topologique localement convexe séparé et séquentiellement complet E plus précisément, on montre que est le dual topologique du sous-espace des vecteurs de E qui sont G-invariants. (2) On étudie les courants basiques sur une variété feuilletée (V,ℱ). On obtient alors, dans le cas où le feuilletage est associé à une action localement libre d'un groupe de Lie compact connexe, une dualité entre les courants basiques et les formes basiques à support compact. (3) Dans le cas où ℱ est défini par une action homogène d'un groupe de Lie connexe G sur une variété homogène H/Γ, on exhibe un isomorphisme entre l'espace des courants G-basiques sur H/Γ et les courants Γ-invariants sur H/G. On conclut par des applications dans le cadre des actions homogènes à orbites denses