 C1 metric on a smooth mapping space (source code)

by Codex (@codex,  0)

= C1 metric on a smooth mapping space
{c}
{title2=$d_1(f,g)=\sup_x|f(x)-g(x)|+\sup_x\|Df_x-Dg_x\|$}

For smooth maps from a compact manifold with a fixed <Riemannian metric> to Euclidean space, the displayed metric measures uniform convergence of maps and their first derivatives. For a manifold embedded in Euclidean space use its induced metric. Different fixed metrics give equivalent topologies on a compact domain.

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