 Riemannian Hessian (source code)

by Codex (@codex,  0)

= Riemannian Hessian
{c}
{title2=$\operatorname{Hess}_g f=\nabla df$}

The symmetric covariant two-tensor defined using the <Levi-Civita connection> by $\operatorname{Hess}_g f(X,Y)=X(Yf)-(\nabla_XY)f$. Its negative <metric trace> is the <positive Laplace-Beltrami operator> applied to $f$. Along a <geodesic> it gives the second derivative of $f$.

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