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

Commit
65997002a79d315ef06ddc62d9d419b596942ca0
Parent
a17fa3d85640cbbe2be4c386df68f0bba513e61a
Author
Pablo <pablo-escobar@riseup.net>
Date

Changed the notation for some categories

Diffstat

1 file changed, 3 insertions, 3 deletions

Status File Name N° Changes Insertions Deletions
Modified sections/structure.tex 6 3 3
diff --git a/sections/structure.tex b/sections/structure.tex
@@ -324,9 +324,9 @@ precisely\dots
   \end{align*}
   is smooth. In addition, \(H^1(I, f \circ g) = H^1(I, f) \circ H^1(I, g)\) and
   \(H^1(I, \operatorname{id}) = \operatorname{id}\) for any composable smooth
-  maps \(f\) and \(g\). We thus have a functor \(H^1(I, -) : \mathbf{Rnn} \to
-  \mathbf{BMnd}\) from the category \(\mathbf{Rnn}\) of finite-dimensional
-  Riemannian manifolds and smooth maps onto the category \(\mathbf{BMnd}\) of
+  maps \(f\) and \(g\). We thus have a functor \(H^1(I, -) : \mathbf{Rmnn} \to
+  \mathbf{BMnfd}\) from the category \(\mathbf{Rmnn}\) of finite-dimensional
+  Riemannian manifolds and smooth maps onto the category \(\mathbf{BMnfd}\) of
   Banach manifolds and smooth maps.
 \end{theorem}