Parallelogram space
Abstract
Two pairs of parallel geodesic intervals can be generated from two such intervals with a common endpoint by suitable application of parallel transfer. When the connection coefficients are symmetric, a parallelogramlike figure with a closed perimeter can be constructed with the two pairs of sides. When the connection coefficients are asymmetric, combining the two pairs of parallel intervals yields a figure with a coordinate gap. To avoid an open perimeter, a fiber that contains many coordinatelike labels is constructed for each point. Then the gap can occur in the fiber of a single point. Thus a closed figure is obtained even when the connection is asymmetric. A process to obtain the coordinatelike quantities in the fiber of one point with respect to a nearby point is described. A discussion of transformations of the coordinatelike quantities follows and the fundamental curvaturelike quantity is obtained.
 Publication:

General Relativity and Gravitation
 Pub Date:
 May 1995
 DOI:
 10.1007/BF02105075
 Bibcode:
 1995GReGr..27..495S