Riemannian Geometry course project on the manifold H¹(I, M) of class H¹ curves on a Riemannian manifold M and its applications to the geodesics problem
Corrected the statement about energy being a Morse function
I'm not sure I understand what a Morse function is supposed to be
1 file changed, 2 insertions, 3 deletions
| Status | File Name | N° Changes | Insertions | Deletions |
| Modified | sections/applications.tex | 5 | 2 | 3 |
diff --git a/sections/applications.tex b/sections/applications.tex @@ -458,9 +458,8 @@ developed in here, by using of the Hessian form \(d^2 E_\gamma\) we can place definition~\ref{def:morse-index} in the broader context of Morse theory. In fact, the geodesics problems and the energy functional where among Morse's original proposed applications. Proposition~\ref{thm:energy-is-morse-function} -amounts to a proof that \(E\) is a Morse function, while -definition~\ref{def:morse-index} amounts to the definition of the Morse index -of the function \(E\) at a critical point \(\gamma\). +and definition~\ref{def:morse-index} amount to a proof that the Morse index of +\(E\) at a critical point \(\gamma\) is well defined. We are now ready to state Morse's index theorem.