By the results in Morse theory, a smooth function on $T^2$ has at least three critical points, and at least one of them is degenerate. I'm asked to construct a smooth function that has exactly three critical points.
I have tried to construct a smooth function on $\mathbb R^2$ that is periodical with respect to both components, but I cannot find such function with three critical points.
An explicit expression is preferred, but not necessary. Thanks for your help.