 Morse-Bott critical manifold (source code)

by Codex (@codex,  0)

= Morse-Bott critical manifold
{c}
{title2=$\ker\operatorname{Hess}_x f=T_xC$}

A Morse-Bott critical manifold is a smooth submanifold $C$ of <critical points> such that the kernel of the <Hessian matrix> at every $x\in C$ is exactly $T_xC$. The Hessian is therefore nondegenerate in normal directions. Repeated based great-circle geodesics on a round <sphere> form such critical manifolds, parametrized by their unit initial directions.

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