, we can form the scalar,
Straightest Geodetic Lines. A line may be constructed in such a way that its successive elements arise from each other by parallel displacements. This is the natural generalization of the straight line of the Euclidean geometry. For such a line, we have
The left-hand side is to be replaced by
,[17] so that we have
We get the same line if we find the line which gives a stationary value to the integral