= Endpoint-vanishing normal Jacobi fields have dimension at most n-1
{title2=$\dim\{J\perp\dot\gamma:J(0)=J(1)=0\}\le n-1$}
In dimension $n\ge2$, along a nonconstant <geodesic>, such a <Jacobi field> is determined injectively by $D_tJ(0)$, which lies in the $(n-1)$-dimensional normal space. On the round unit sphere the geodesic from a point to its antipode, parametrized with speed $\pi$ on $[0,1]$, has fields $J(t)=\sin(\pi t)E(t)$ for all parallel normal fields $E$, attaining the bound. For a constant geodesic the endpoint-vanishing Jacobi field space is zero.
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