Physical space-time allows of a metric of asymmetrical properties because of the unidirection of time. The simplest possible asymmetrical generalization of Riemannian metric is considered. The study of this metric is here mainly confined to the mathematical aspects. However, the physical consequences by application to space-time are obvious, and may be of interest by leading directly to a description of the electromagnetic field. A close formal connection with five-dimensional Riemannian geometry is shown, which might carry interest for the physical interpretation of five-dimensional relativity.

• Received 1 October 1940

DOI:https://doi.org/10.1103/PhysRev.59.195