Hyperbolic U sub 4 Manifolds with Local Duality.

摘要

The author uses the decomposition of the Riemann/Cartan curvature 2-forms omega sup(ij) in terms of their irreducible parts under the Lorentz group to examine the irreducible content of self- and anti-self double dual curvature forms omega sup(+-ij) and their further refinements involving left and right duals. In the case of local duality (i.e. omega sup(ij)= omega sup(+-ij) locally), some consequences to curvature and torsion are easily derived in this way. As Riemann/Cartan space-times (U sub 4 -space times) are subject to generalized gravity theories, some (vacuum) field equations proposed there are also taken into consideration. As an application of the various decompositions of curvature and torsion the author points out their utility in the search of exact solutions of U sub 4 -field equations. To simplify notations and calculations, the calculus of exterior forms is used throughout. (Atomindex citation 13:692969)