Riemannian vectorial collineations along with current Killing conservation are shown to lead to tensorial collineations for the energystress tensor in general relativity and in Einstein-Cartan Weyssenhoff fluid cosmology. PACS numbers : 0420,0450. Departamento de F́ısica Teórica Instituto de F́ısica UERJ Rua São Fco. Xavier 524, Rio de Janeiro, RJ Maracanã, CEP:20550-003 , Brasil. e-mail.: garcia...

We start by presenting the general set of structure equations for 1+3 threading spacetime decomposition in 4 dimensions, valid any theory gravitation based on a metric compatible affine connection. then apply these to study cosmological solutions Einstein-Cartan which matter is modeled perfect fluid with intrinsic spin. It shown that tensor can be described generic FLRW solution. However, due p...

In this paper, we consider an autonomous two-dimensional ODE Kolmogorov-type system with three parameters, which is a particular of the general predator–prey systems Holling type II. By reformulating as set two second-order differential equations, investigate nonlinear dynamics from Jacobi stability point view using Kosambi–Cartan–Chern (KCC) geometric theory. We then determine connection, Berw...

The cosmological implications of the Covariant Canonical Gauge Theory Gravity (CCGG) are investigated. CCGG is a Palatini theory derived from first principles using canonical transformation formalism in covariant Hamiltonian formulation. Einstein-Hilbert thereby extended by quadratic Riemann-Cartan term Lagrangian. Moreover, requirement conservation stress-energy tensor leads to necessary prese...

In this work, we will consider an autonomous three-dimensional quadratic system of first-order ordinary differential equations, with five parameters and symmetry relative to the z-axis, which generalize Hopf–Langford system. By reformulating as a two second-order equations using Kosambi–Cartan–Chern (KCC) geometric theory, investigate from perspective Jacobi stability. We compute invariants KCC...

Abstract Holomorphically homogeneous Cauchy–Riemann (CR) real hypersurfaces $M^3 \subset \mathbb{C}^2$ were classified by Élie Cartan in 1932. In the next dimension, we complete classification of simply-transitive Levi non-degenerate $M^5 \mathbb{C}^3$ using a novel Lie algebraic approach independent any earlier classifications abstract algebras. Central to our is new coordinate-free formula fo...

Külshammer, Olsson and Robinson conjectured that a certain set of numbers determined the invariant factors of the `-Cartan matrix for Sn (equivalently, the invariant factors of the Cartan matrix for the Iwahori-Hecke algebra Hn(q), where q is a primitive `th root of unity). We call these invariant factors Cartan invariants. In a previous paper, the second author calculated these Cartan invarian...

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...