On a Completely Antisymmetric Cartan Torsion Tensor
نویسنده
چکیده
We discuss the general structure of metric geometries, and how metricity implies the complete antisymmetry of Cartan tensor; an application in the frame of Lie group theory is given. Interpretations of the completely antisymmetric torsion in physical models are reviewed.
منابع مشابه
On a Completely Antisymmetric Cartan Tensor
Theory of General Relativity is considered from the point of view of its general structure; it has been showed that if one assumes any connection to be a metric connection then Cartan tensor must necessary be completely antisymmetric, and an example of application is considered in the case of Lie group theory. Under a geometrical point of view, Cartan tensor is thought to represent the Torsion ...
متن کاملOn the problem of Unicity in Einstein-Sciama-Kibble Theory
We consider the ESK theory, based on the principle for which the space is filled with matter fields in such a way that Cartan torsion is spin; in the geometry in which Cartan torsion tensor is completely antisymmetric then spin has to be completely antisymmetric as well: we will show how spin complete antisymmetry constraints the form of possible matter field theories as to allow the special ca...
متن کاملNew Gauge Symmetry in Gravity and the Evanescent Role of Torsion
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...
متن کاملA Note on Flat Metric Connections with Antisymmetric Torsion
In this short note we study flat metric connections with antisymmetric torsion T 6= 0. The result has been originally discovered by Cartan/Schouten in 1926 and we provide a new proof not depending on the classification of symmetric spaces. Any space of that type splits and the irreducible factors are compact simple Lie group or a special connection on S. The latter case is interesting from the ...
متن کاملAn intrinsic volume functional on almost complex 6-manifolds and nearly Kähler geometry
Let (M, I) be an almost complex 6-manifold. The obstruction to integrability of almost complex structure (socalled Nijenhuis tensor) N : Λ0,1(M)−→ Λ(M) maps a 3-dimensional bundle to a 3-dimensional one. We say that Nijenhuis tensor is non-degenerate if it is an isomorphism. An almost complex manifold (M, I) is called nearly Kähler if it admits a Hermitian form ω such that ∇(ω) is totally antis...
متن کامل