Gravitational stability of torsion and inflaton potential in a fourdimensional spacetime de Sitter solution in scalar-tensor cosmology where Cartan torsion propagates is investigated in detail. Inflaton and torsion evolution equations are derived by making use of a Lagrangean method. Stable and unstable modes for torsion and inflatons are found. Present astrophysical observations favour a stabl...

We explore the different geometric structures that can be constructed from the class of pairs of 2nd order PDE’s that satisfy the condition of a vanishing generalized Wünschmann invariant. This condition arises naturally from the requirement of a vanishing torsion tensor. In particular, we find that from this class of PDE’s we can obtain all four-dimensional conformal Lorentzian metrics as well...

Two special Finsler spaces have been introduced and investigated, namely R-recurrent Finsler space and concircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of the present paper: (i) a concircularly flat Finsler manifold is necessarily of co...

A propagating torsion model is derived from the requirement of compatibility between minimal action principle and minimal coupling procedure in Riemann-Cartan spacetimes. In the proposed model, the trace of the torsion tensor is derived from a scalar potential that determines the volume element of the spacetime. The equations of the model are write down for the vacuum and for various types of m...

A limiting diagram for the Segre classification of the energy-momentum tensor is obtained and discussed in connection with a Penrose specialization diagram for the Segre types. A generalization of the coordinate-free approach to limits of Paiva et al. to include non-vacuum space-times is made. Geroch’s work on limits of space-times is also extended. The same argument also justifies part of the ...

Abstract. We calculate correlation functions of the (charge) density of zeroes of Gaussian distributed vector fields. We are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract Riemann Cartan or Riemannian manifold. As an application, we discuss one and two point functions. The zeroes of a two dimensional Gaussian vector field model the di...

We calculate correlation functions of the (signed) density of zeros of Gaussian distributed vector fields. We are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract Riemann Cartan or Riemannian manifold. As an application, we discuss one and twopoint functions. The zeros of a two-dimensional Gaussian vector field model the distribution of...

Abstract Tensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus attention due to the fundamental rôle they play for extended geometry. In present paper, we examine tensor which super-extensions over-extended (often, hyperbolic...

We construct and study in detail various dual pairs acting on some Fock spaces between a finite dimensional Lie group and a completed infinite rank affine algebra associated to an infinite affine Cartan matrix. We give explicit decompositions of a Fock representation into a direct sum of irreducible isotypic subspaces with respect to the action of a dual pair, present explicit formulas for the ...

We address the integrability conditions of the inverse problem of the calculus of variations for time-dependent SODE using the Spencer version of the Cartan–Kähler theorem. We consider a linear partial differential operator P given by the two Helmholtz conditions expressed in terms of semi-basic 1-forms and study its formal integrability. We prove that P is involutive and there is only one obst...