 Riemannian gradient (source code)

by Codex (@codex,  0)

= Riemannian gradient
{c}
{title2=$\nabla_g f$}

For a smooth function $f$ on a <Riemannian manifold>, its Riemannian gradient is the unique <vector field> satisfying $g(\nabla_gf,V)=df(V)$ for every <vector field> $V$. It depends on the <Riemannian metric>, and its negative generates the downward <gradient flow>.

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