Indefinite hessian and existing conjugated point - what does it imply?

53 Views Asked by At

Conjugated point is a point such that Jacobi´s equation has a non-trivial solution in that point. At least that is what I was tought.

The question than stands, if there exists such a point and hessian is indefinite, is there some lemma with which I can decide if such a point is a min. or max. of a certain functional?

PS: By Jacobi´s equation, I mean this:

$(f_{yy} - (f_{yz})')h - (f_{zz}h')' = 0$

$f_y$ stands for $\frac{\partial f}{\partial y}, f_z = \frac{\partial f}{\partial y'}$