= Locally maximally symmetric space
{title2=$\dim\mathfrak{isom}_{\rm local}=n(n+1)/2$}
An $n$-dimensional <Riemannian manifold> is locally maximally symmetric if its local <Killing vector fields> attain the <dimension bound for Killing vector fields> $n(n+1)/2$. This is equivalent to constant <sectional curvature>. Positive, zero and negative <sectional curvature> give local <spherical geometry>, <Euclidean geometry> and <hyperbolic geometry>, respectively. Global identifications can reduce the number of globally defined <isometries> without changing this local property. The spatial slices of an <FLRW metric> have this property.
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