For example, let be the torus. Let . Then we know that a map given by
is a parametrization for almost all of . Now, via the projection we get the restriction whose critical sets are determined by
if and only if .
These two values for give the critical set
which represent two extremal circles over the torus .
Observe that the Hessian for this function is which clearly it reveals itself as of at the tagged circles, making the critical point degenerate, that is, showing that the critical points are not isolated.
|Date of creation||2013-03-22 15:44:12|
|Last modified on||2013-03-22 15:44:12|
|Last modified by||juanman (12619)|
|Synonym||functions with critical loops|