Let $(M,g)$ be a smooth Riemannian manifold of dimension $n \geq 2$, let $p \in M$, and let $\Omega_p \subset M$ be the regular domain of geodesic polar coordinates centered at $p$. Let
be the orthogonal complement to the radial direction, and let
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\begin{align*}
A(t):E_t &\to E_t
\end{align*}
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be the radial shape operator along $\gamma$. Assume $A(t)$ is self-adjoint with respect to $g_{\gamma(t)}$ and satisfies the radial matrix Riccati equation