follows from (86); this is the Riemann curvature tensor of the fourth rank, whose properties of symmetry we do not need to go into. Its vanishing is a sufficient condition (disregarding the reality of the chosen co-ordinates) that the continuum is Euclidean.
By contraction of the Riemann tensor with respect to the indices
,
, we obtain the symmetrical tensor of the second rank,
The last two terms vanish if the system of co-ordinates is so chosen that
. From