Specifically, call a smooth vector field along a smooth curve parallel along if identically. Fix a curve with and . to parallel transport a vector to a vector in along , first extend to a vector field parallel along , and then take the value of this vector field at .
Specifically, call a smooth vector field along a smooth curve parallel a,long if identically. Fix a curve with and  to parallel transport a vector to a ,vector in along  first extend to a vector fie.ld parallel along  and then take the value of this vector field at .