= Solution
Use precisely the stated convention for the <Riemann curvature tensor>, and let $D=\nabla_T$. The <geodesic equation> says $\nabla_TT=0$ because <proper time> is an <affine parameter>. The commuting variation and the <torsion-free connection> give
$$
D^2S=\nabla_T\nabla_ST=\nabla_S\nabla_TT+R(T,S)T+\nabla_{[T,S]}T=R(T,S)T.
$$
Thus the <geodesic deviation> equation is
$$
\boxed{\nabla_T^2S=R(T,S)T,\qquad (D^2S)^a=R^a{}_{bcd}T^bT^cS^d.}
$$
Here $(R(X,Y)Z)^a=R^a{}_{bcd}Z^bX^cY^d$. Declaring this index convention fixes the sign: writing $R(S,T)T$ instead would require a minus sign. A <deviation vector> satisfying this equation is a <Jacobi field>.
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