= Deviation vector
{title2=$S=F_*\partial_s$}
For a <geodesic variation> $F(s,\tau)$, the <deviation vector> $S=F_*\partial_s$ describes infinitesimal separation at equal parameter values. With $T=F_*\partial_\tau$, commuting parameter derivatives give $[S,T]=0$. A <torsion-free connection> then gives $\nabla_TS=\nabla_ST$. For an affinely parametrized variation, <geodesic deviation> states $\nabla_T^2S=R(T,S)T$ with the convention $R(X,Y)Z=\nabla_X\nabla_YZ-\nabla_Y\nabla_XZ-\nabla_{[X,Y]}Z$.
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