Curvature tensors and unified field equations on \(SEX_ n\)
The authors begin with a brief review of Einstein's unified field theory as formulated by Hlavaty (in the general n-dimensional case). They then proceed to define a modified theory based on the Einstein-Hlavaty approach which consists of an n-dimensional manifold endowed with a connection satisfying two properties (called the ``Einstein'' and ``semisymmetric'' properties by the authors) and a (in general non- symmetric) metric tensor linked by a certain system of differential equations. The appropriately endowed manifold is, perhaps unfortunately, denoted by the symbols \(SEX_ n\). They then proceed to derive various algebraic and differential (Ricci and Bianchi-type) identities on their manifold and to set up field equations similar to the Einstein-Hlavaty system. The paper is concluded by a demonstration that these field equations actually have a solution. Although the general approach is sometimes confusing and a little old fashioned, perhaps the most confusing thing is that the same round bracket symbol is used for both the symmetrisation and skew- symmetrisation operationsö Also strange was the fact that five of the references contained only the authors' name and the year of publication. The approach throughout is geometrical and the authors indicated little or nothing to suggest an application to physics (except that which is implicitly contained in the original Einstein formulation).
scientific article; zbMATH DE number 4064005