Differential Forms on Riemannian (Lorentzian) and Riemann-Cartan Structures and Some Applications to Physics
arXiv:0712.3067
Abstract
In this paper after recalling some essential tools concerning the theory of differential forms in the Cartan, Hodge and Clifford bundles over a Riemannian or Riemann-Cartan space or a Lorentzian or Riemann-Cartan spacetime we solve with details several exercises involving different grades of difficult. One of the problems is to show that a recent formula appearing in the literature for the exterior covariant derivative of the Hodge dual of the torsion 2-forms is simply wrong. We believe that the paper will be useful for students (and eventually for some experts) on applications of differential geometry on physical problems. A detailed account of the issues discussed in the paper appears in the table of contents.
Some few important misprints appearing in the version of the paper published in AFLB (in a special issue dedicated to torsion) are corrected