1,721,047 research outputs found
SU(3)-holonomy metrics from nilpotent Lie groups
No full textOne way of producing explicit Riemannian 6-manifolds with holonomy SU(3) is by integrating a flow of SU(2)-structures on a 5-manifold, called the hypo evolution flow. In this paper we classify invariant hypo SU(2)-structures on nilpotent 5-dimensional Lie groups. We characterize the hypo evolution flow in terms of gauge transformations, and study the flow induced on the variety of frames on a Lie algebra taken up to automorphisms. We classify the orbits of this flow for all hypo nilpotent structures, obtaining several families of cohomogeneity one metrics with holonomy contained in SU(3). We prove that these metrics cannot be extended to a complete metric, unless they are fla
Intrinsic torsion in quaternionic contact geometry
No full textWe investigate quaternionic contact (qc) manifolds from the point of view of intrinsic torsion. We argue that the natural structure group for this geometry is a non-compact Lie group K containing Sp(n)H∗, and show that any qc structure gives rise to a canonical K-structure with constant intrinsic torsion, except in seven dimensions, when this condition is equivalent to integrability in the sense of Duchemin. We prove that the choice of a reduction to Sp(n)H∗ (or, equivalently, a complement of the qc distribution) yields a unique K-connection satisfying natural conditions on torsion and curvature. We show that the choice of a compatible metric on the qc distribution determines a canonical reduction to Sp(n)Sp(1) and a canonical Sp(n)Sp(1)-connection whose curvature is almost entirely determined by its torsion. We show that its Ricci tensor, as well as the Ricci tensor of the Biquard connection, has an interpretation in terms of intrinsic torsion
Cohomogeneity one Einstein-Sasaki 5-manifolds
No full textWe consider hypersurfaces in Einstein-Sasaki 5-manifolds which are tangent
to the characteristic vector field. We introduce evolution equations that can be used to reconstruct the 5-dimensional metric from such a hypersurface, analogous to the (nearly)hypo and half-flat evolution equations in higher dimensions. We use these equations to classify Einstein-Sasaki 5-manifolds of cohomogeneity one
Análisis del kirchnerismo desde el enfoque de populismo macroeconómico de Dornbusch y Edwards
Full text linkFil: Ganam Conti, Diego Martín. Universidad de San Andrés. Departamento de Economía; Argentina.Fil: Ruiz Moreno, Iván. Universidad de San Andrés. Departamento de Economía; Argentina
Special holonomy and hypersurfaces
Full text linkFrom the introduction: In Chapter 1 we explain
in detail the background that we sketched at the beginning of this introduction;
no new results appear in this chapter.[...]In Chapter 2 we study the local geometry of hypersurfaces inside spin
Riemannian manifolds M admitting a parallel spinor, as well as abstract
G-structures defined by a generalized Killing spinor.[...]Chapter 3 is independent of Chapter 2; it is aimed at understanding
Salamon’s “dictionary” technique from a theoretical point of view.[...]In Chapter 4 we apply the techniques of Chapter 3 to produce invariant
special geometries.[...]Chapter 5 is independent of Chapter 3, and uses little of Chapter 4;
it deals with hypo geometry, i.e. the geometry defined by a generalized
Killing spinor in five dimensions
The Ricci-flatness that lurks in weight
Full text linkWe introduce two constructions to obtain left-invariant Ricci-flat pseudo-Riemannian metrics on nilpotent Lie groups, one based on gradings, the other on filtrations, both depending on the combinatorics of the set of weights.
As an application, we show that every nilpotent Lie algebra of dimension up to and every nice nilpotent Lie algebra of dimension up to admit an indefinite Ricci-flat metric.18 pages, 3 tables; includes an ancillary file with 8 more table
Embedding into manifolds with torsion
No full textWe introduce a class of special geometries associated to the choice of a differential graded algebra contained in Λ*Rn. We generalize some known embedding results, that effectively characterize the real analytic Riemannian manifolds that can be realized as submanifolds of a Riemannian manifold with special holonomy, to this more general context. In particular, we consider the case of hypersurfaces inside nearly-Kähler and α-Einstein-Sasaki manifolds, proving that the corresponding evolution equations always admit a solution in the real analytic case. © 2010 Springer-Verlag
Linear perturbations of metrics with holonomy Spin(7)
No full textWe apply the method of linear perturbations to the case of Spin(7)-structures, showing that the only nontrivial perturbations are those determined by a rank one nilpotent matrix. We consider linear perturbations of the Bryant-Salamon metric on the spin bundle over S4 that retain invariance under the action of Sp(2), showing that the metrics obtained in this way are isometric
Calabi-Yau cones from contact reduction
No full textWe consider a generalization of Einstein-Sasaki manifolds, which we characterize in terms both of spinors and differential forms, that in the real analytic case corresponds to contact manifolds whose symplectic cone is Calabi-Yau. We construct solvable examples in seven dimensions. Then, we consider circle actions that preserve the structure, and determine conditions for the contact reduction to carry an induced structure of the same type. We apply this construction to obtain a new hypo-contact structure on S^2\times T^3
Einstein almost cokähler manifolds
No full textWe study an odd-dimensional analogue of the Goldberg conjecture for compact Einstein almost Kähler manifolds. We give an explicit non-compact example of an Einstein almost cokähler manifold that is not cokähler. We prove that compact Einstein almost cokähler manifolds with nonnegative *-scalar curvature are cokähler (indeed, transversely Calabi–Yau); more generally, we give a lower and upper bound for the *-scalar curvature in the case that the structure is not cokähler. We prove similar bounds for almost Kähler Einstein manifolds that are not Kähler
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