I'm searching for stationary points of a multi-variable function which is defined on a manifold. To do this I parametrize my manifold and then differentiate the function with respect to the associated parameters.
I'm wondering if the stationary points of the function depend on the parametrization that we choose or not?
To specify the question to my case, the function that I'm looking at is an energy depending on some coefficients of a wave function. This coefficients are the elements of an orthogonal matrix. So I need to parametrize the orthogonal matrix manifold. The two parametrizations that I'm currently using are:
- A product of Givens rotations
- An exponential of an anti-symmetric matrix
If anyone could help me or give me a good reference for this problem, it would be really appreciated.