= Locally symmetric Riemannian manifold
{title2=$\nabla R=0$}
A <Riemannian manifold> is locally symmetric when its <Riemann curvature tensor> is parallel for the <Levi-Civita connection>. Along a <geodesic>, <parallel transport> then conjugates the <Jacobi curvature operator> at the initial point to the operator at every later point. Thus its <eigenvalues> stay constant. The condition is local and does not assert that global point reflections extend to isometries of the whole manifold.
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