Showing papers in "Journal of Geometry and Physics in 2006"

TL;DR: In this paper, the notion of implicit Lagrangian systems with both holonomic and nonholonomic constraints is introduced. And the definition of implicit L-C circuits is presented.

TL;DR: In this article, the Lagrange-d'Alembert-Pontryagin principle was extended to implicit Lagrangian systems with constraints and external forces, and a variational formulation incorporating the generalized Legendre transformation was proposed.

TL;DR: In this article, a unit timelike quaternion is used to represent a rotation in the Minkowski 3-space, and a Lorentzian rotation matrix is expressed with a time-like Quaternion.

TL;DR: It is shown that there is an alternative characterisation of conformally Einstein metrics based on the tractor connection associated with the normal conformal Cartan bundle, which plays a key role in constructing some of the invariants.

TL;DR: The notion of pseudo-Riemannian spectral triple was introduced in this paper, which generalizes the notion of spectral triple and allows for a treatment of pseudo Riemannians within a non-commutative setting.

TL;DR: In this paper, a survey of the relation between perturbative renormalization and motivic Galois theory is presented, and the main result is that all quantum field theories share a common universal symmetry realized as a motivated Galois group, whose action is dictated by the divergences and generalizes that of the renormalisation group.

TL;DR: In this paper, the inner fluctuations of the spectral action can be computed as residues and the counterterms for the Feynman graphs with fermionic internal lines are given for geometries of dimension less than or equal to four.

TL;DR: In this paper, a relative version of T -duality in generalized complex geometry is proposed as a manifestation of mirror symmetry, and a bijective correspondence between ∇ -semi-flat generalized almost complex structures on the total space of a real manifold and ∇ ∨ semi-flat GAs on the manifold is established.

TL;DR: In this paper, it was conjectured that the classical bosonic string in AdS times a sphere has a special action variable which corresponds to the length of the operator on the field theory side.

TL;DR: In this article, the transformation of a p -harmonic morphism into a q-harmonic one via biconformal change of the domain metric and/or conformal changes of the codomain metric is studied.

TL;DR: Bailey and Eastwood as discussed by the authors characterized n th-order ODEs for which the space of solutions M is equipped with a particular paraconformal structure, which is a splitting of the tangent bundle as a symmetric tensor product of rank-two vector bundles.

TL;DR: In this article, the Mielke-Baekler model for zero, positive and negative effective cosmological constant was obtained for metric affine gravity with torsion and non-metricity.

TL;DR: Using general non-skew symmetric classical r -matrices with a spectral parameter, the authors constructed new quantum spin chains that generalize famous Gaudin spin chains.

TL;DR: In this paper, the authors studied the decomposition of forms induced by a generalized complex structure, giving a complete description of the bundles involved and, around regular points, of the operators ∂ and ∂ ¯ associated to the structure.

TL;DR: In this paper, Ugalde generalized Connes' result to n -dimensional manifold without boundary and showed that it can be computed using Wodzicki's 1-density invariant.

TL;DR: In this paper, an approach to the Dolbeault sequence for several quaternionic variables based on symmetries and representation theory is presented, and it is shown that the resolution of the Cauchy-Fueter system obtained algebraically, via Grobner bases techniques, is equivalent to the one obtained by R.J. Baston.

TL;DR: For a certain class of perturbations of the equation u t = f ( u ) u x, this article proved the existence of change of coordinates, called quasi-Miura transformations, that reduce these perturbed equations to the unperturbed one.

TL;DR: In this article, the authors introduced generalisations of pp-waves, on one hand by allowing the vector field to be recurrent and on the other hand by weakening the curvature condition, which can be expressed in terms of the screen bundle of the manifold and how they are related to the screen holonomy.

TL;DR: In this paper, the authors review the power-counting analysis of field theories on the Moyal plane in momentum space and their recent renormalisation proof of noncommutative ϕ 4 -theory based on renormalization group techniques for dynamical matrix models.

TL;DR: In this article, it was shown that the Penrose limit of a spacetime along a homogeneous geodesic is a Cahen-Wallach space, and that a reductive homogeneous spacetime with the same property is a plane wave spacetime.

TL;DR: In this paper, the authors prove a compactness theorem for gradient Ricci solitons, where the curvatures are uniformly bounded from below, with uniformly lower bounded volume and with uniformly upper bounded diameter.

TL;DR: The connection between non-commutative geometry and physics is discussed in this article, where the authors show the road from canonical quantization to Lie groupoids and Lie algebroids via Mackey's imprimitivity theorem and its symplectic counterpart.

TL;DR: In this article, it was shown that any equation from the Davey-Stewartson hierarchy induces an infinite family of geometrically different deformations of tori in R 4 preserving the Willmore functional.

TL;DR: Tauraso et al. as discussed by the authors showed that the Lefschetz number of any continuous map f on an infra-nilmanifold with holonomy group Ψ is L ( f ) = 1 | Ψ | ∑ A ∈ Ψ det (A ∗ − f ∗ ) det A ∗.

TL;DR: In this article, the existence of affine and non-Novikov structures on two-step solvable Lie algebras has been studied and shown to be solvable.

TL;DR: In this article, a differential calculus for subalgebras of the Moyal algebra on R 4 was proposed, starting from a redundant differential calculus on the moyal algebra, which is suitable for reduction.

TL;DR: Krasilshchik and Vinogradov as mentioned in this paper considered PDEs as infinite-dimensional manifolds with involutive distributions and considered their special morphisms called differential coverings, which include constructions like Lax pairs and Backlund transformations.

TL;DR: In this article, the second order differential operator associated to the r-th elementary symmetric function (Sr) on the eigenvalues of the second fundamental form of a hypersurface was computed for the case of a constant higher order mean curvature, and the resulting formula was used to study both r-maximal spacelike hypersurfaces of M¯, as well as, in the presence of such curvatures, constraints on the sectional curvatures that also suffice to guarantee the umbilicity of M.

TL;DR: In this article, the hyper-Kahler quotient construction is applied to Lie groups with a left invariant hyper-kahler structure under the action of a closed abelian subgroup by left multiplication.

TL;DR: In this paper, a condition for an observer to be comoving with another observer in general relativity, based on the concept of light-like simultaneity, is given. But the conditions for comoving are not defined.