= Three-critical-point function on a torus
{title2=$h(u,v)=\sin u\sin v\sin(u-v)$}
Take $u,v$ modulo $\pi$; shifting either coordinate by $\pi$ leaves $h$ unchanged. Its partial derivatives are $h_u=\sin v\sin(2u-v)$ and $h_v=\sin u\sin(u-2v)$. The only <critical points> are $(0,0)$, $(\pi/3,2\pi/3)$ and $(2\pi/3,\pi/3)$. The latter are a nondegenerate minimum and maximum, with values $\mp3\sqrt3/8$. At the origin the leading cubic is $uv(u-v)$, linearly equivalent to a <monkey saddle>; its <critical point> is isolated but degenerate. Thus three smooth <critical points> coexist with the Morse lower bound of four for the <torus>.
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