= Dimension bound for Killing vector fields
{title2=$\dim\mathfrak{kill}(M,g)\leq n(n+1)/2$}
On a connected $n$-dimensional <pseudo-Riemannian manifold>, evaluation of a <Killing vector field> and its first derivative is injective by <Killing transport>. The value has $n$ components and the <Killing equation> makes the derivative an antisymmetric two-tensor with $n(n-1)/2$ components. Their sum gives the bound. Flat metrics attain it through $\xi_a=A_a+B_{ab}x^b$ with $B_{ab}=-B_{ba}$. Connectedness is essential for a uniform global bound in terms of $n$: independent fields can be supported on different connected components.
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