Quantifying The Difference From A Parallelogram
The length of this last geodesic constructed connecting the remaining points A′B′ may in general be different than the length of the base AB. This difference is measured by the Riemann curvature tensor. To state the relationship precisely, let AA′ be the exponential of a tangent vector X at A, and AB the exponential of a tangent vector Y at A. Then
where terms of higher order in the length of the sides of the parallelogram have been suppressed.
Read more about this topic: Levi-Civita Parallelogramoid
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