The book “Handbook of Finsler geometry” has been included with a CD containing an elegant Maple package, FINSLER, for calculations in Finsler geometry. Using this package, an example concerning a Finsler generalization of Einstein’s vacuum field equations was treated. In this example, the calculation of the components of the hv-curvature of Cartan connection leads to wrong expressions. On the o...

In scalar-tensor theories of gravity with torsion, the gravitational field is described in terms of a symmetric metric tensor g, a metriccompatible connection ∇ with torsion, and a scalar field φ. The main aim is to explore an interaction of a charged perfect fluid and a scalar field φ in a background electromagnetic and gravitational field described by {g, ∇, φ}. The interaction is based on an...

A rotating universe represented by the Gödel metric in spacetimes with Cartan torsion is investigated where the Cosmic Microwave Background Radiation (CMBR) is computed from the Gödel rotation of the universe and the spin density of the spinning fluid in EinsteinCartan gravity.The autoparallel equation in Riemann-Cartan spacetime is shown to lead to the evolution equation of the cosmological pe...

The curvature tensor \(\hat{R}\) of a manifold is called harmonic, if it obeys the condition \(\Delta^{\text{(HR)}}\hat{R}=0\), where \(\Delta^{\text{(HR)}}=DD^{\ast} +
 D^{\ast}D\) Hodge–deRham Laplacian. It proved that all solutions Einstein equations in vacuum, as well Einstein–Cartan theory vacuum have harmonic curvature. statement only Einstein’s type \(N\) (describing gravitational r...

If the Einstein-Hilbert action LEH ∝ R is re-expressed in Riemann-Cartan spacetime using the gauge fields of translations, the vierbein field hμ, and the gauge field of local Lorentz transformations, the spin connection Aμα β , there exists a new gauge symmetry which permits reshuffling the torsion, partially or totally, into the Cartan curvature term of the Einstein tensor, and back, via a new...

Let Am,n be the tensor product of Laurent polynomial algebra in m even variables and exterior n odd over complex field C, Witt superalgebra Wm,n Lie superderivations Am,n. In this paper, we classify simple weight modules with finite-dimensional spaces respect to standard Cartan subalgebra Wm,0. Every such module is either a quotient or highest type.

A global monopole in dilatonic Einstein-Cartan gravity is presented. A linearized solution representing a global monopole interacting with a massless dilaton is found where Cartan torsion does not interact with the monopole Higgs field.Computation of the geodesic equation shows that the monopole-dilaton system generates a repulsive gravitational field.The solution is shown to break the linear a...

Oscillating phases in Bianchi type IX anisotropic universes are obtained as linearized solutions of Einstein-Cartan theory of gravity.Instead of making use of Weyssenhoff spinning fluids we addopt axionic torsion matter where the torsion tensor is totally skew-symmetric as in Kalb-Rammond type theories.Spin-torsion,metric and matter density oscillate at different phases. An upper bound oscillat...

The purpose of this note is to provide yet another example of the link between certain conformal geometries and ordinary differential equations, along the lines of the examples discussed by Nurowski [3]. In this particular case, I consider the equivalence problem for 3-plane fields D ⊂ TM on a 6-manifold M satisfying the nondegeneracy condition that D + [D, D] = TM . I give a solution of the eq...