- Commit
- 65997002a79d315ef06ddc62d9d419b596942ca0
- Parent
- a17fa3d85640cbbe2be4c386df68f0bba513e61a
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Changed the notation for some categories
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
Changed the notation for some categories
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}