global-analysis-and-the-banach-manifold-of-class-h1-curvers

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

Diffstat

1 file changed, 1 insertion, 1 deletion

diff --git a/sections/applications.tex b/sections/applications.tex
@@ -38,7 +38,7 @@ point. Without further ado, we prove\dots
   \begin{align*}
     E : H^1(I, M) & \to \mathbb{R} \\
     \gamma
-    & \mapsto \frac{1}{2} \norm{\partial \gamma}_0
+    & \mapsto \frac{1}{2} \norm{\partial \gamma}_0^2
     = \frac{1}{2} \int_0^1 \norm{\dot\gamma(t)}^2 \; \dt
   \end{align*}
   is smooth and \(d E_\gamma X = \left\langle \partial \gamma, \frac\nabla\dt X