May 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995gregr..27..495s&link_type=abstract
General Relativity and Gravitation, Volume 27, Issue 5, pp.495-509
Physics
Scientific paper
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 parallelogram-like 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 coordinate-like 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 coordinate-like quantities in the fiber of one point with respect to a nearby point is described. A discussion of transformations of the coordinate-like quantities follows and the fundamental curvature-like quantity is obtained.
Shurtleff Richard
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