- Commit
- 65246e10823f7943248714cfcdd3a7b5a1024ae1
- Parent
- f09d3c968ceb744a4f9c68e28289da9c4269f747
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Added further details on the abstract isomorphism between H¹(gamma* TM) and H¹(I, R^n)
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, 2 insertions, 2 deletions
| Status | File Name | N° Changes | Insertions | Deletions |
| Modified | sections/structure.tex | 4 | 2 | 2 |
diff --git a/sections/structure.tex b/sections/structure.tex @@ -285,8 +285,8 @@ Finally, we find\dots gives \(H^1(I, M)\) the structure of a \emph{separable} Banach manifold modeled after separable Hilbert spaces, with typical representatives\footnote{Any trivialization of $\gamma^* TM$ induces an - isomorphism $H^1(\gamma^* TM) \isoto H^1(I, \mathbb{R}^n)$.} \(H^1(\gamma^* - TM) \cong H^1(I, \mathbb{R}^n)\). + isomorphism $H^1(\gamma^* TM) \isoto H^1(I \times \mathbb{R}^n) \cong H^1(I, + \mathbb{R}^n)$.} \(H^1(\gamma^* TM) \cong H^1(I, \mathbb{R}^n)\). \end{theorem} The fact that \(\exp_\gamma\) is bijective should be clear from the definition