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

2 files changed, 17 insertions, 5 deletions

diff --git a/references.bib b/references.bib
@@ -33,3 +33,14 @@
    year =      {1988},
    series =    {Lecture Notes in Mathematics},
 }
+
+@article{eells,
+  title={A setting for global analysis},
+  author={James Eells, Jr.},
+  journal={Bulletin of the American Mathematical Society},
+  volume={72},
+  number={5},
+  pages={751--807},
+  year={1966}
+}
+

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -186,11 +186,12 @@ unless explicitly stated otherwise. Speaking of examples\dots
 
 \begin{example}
   The group of units \(A^\times\) of a Banach algebra \(A\) is an open subset,
-  so that it constitutes a Banach manifold modeled after \(A\). In particular,
-  given a Banach space \(V\) the group \(\GL(V)\) of continuous linear
-  isomorphisms \(V \to V\) is a -- possibly non-separable -- Banach manifold
-  modeled after the space \(\mathcal{L}(V) = \mathcal{L}(V, V)\) under the
-  operator norm: \(\GL(V) = \mathcal{L}(V)^\times\).
+  so that it constitutes a Banach manifold modeled after \(A\)
+  \cite[sec.~3]{eells}. In particular, given a Banach space \(V\) the group
+  \(\GL(V)\) of continuous linear isomorphisms \(V \to V\) is a -- possibly
+  non-separable -- Banach manifold modeled after the space \(\mathcal{L}(V) =
+  \mathcal{L}(V, V)\) under the operator norm: \(\GL(V) =
+  \mathcal{L}(V)^\times\).
 \end{example}
 
 \begin{example}