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

references.bib (1389B)

 1 @book{klingenberg,
 2   title={Riemannian Geometry},
 3   author={Wilhelm Klingenberg},
 4   isbn={9783110905120},
 5   series={De Gruyter Studies in Mathematics},
 6   year={2011},
 7   publisher={De Gruyter}
 8 }
 9 
10 @book{lang,
11    title =     {Fundamentals of Differential Geometry},
12    author =    {Serge Lang},
13    publisher = {Springer},
14    isbn =      {9780387985930},
15    year =      {1999},
16    series =    {Graduate Texts in Mathematics},
17    edition =   {1},
18 }
19 
20 @misc{unitary-group-strong-topology,
21   doi = {10.48550/ARXIV.1309.5891},
22   author = {Martin Schottenloher},
23   title = {The Unitary Group In Its Strong Topology},
24   publisher = {arXiv},
25   year = {2013},
26 }
27 
28 @book{palais,
29    title =     {Critical Point Theory and Submanifold Geometry},
30    author =    {Richard Palais, Chuu-lian Terng},
31    publisher = {Springer},
32    isbn =      {3540503994},
33    year =      {1988},
34    series =    {Lecture Notes in Mathematics},
35 }
36 
37 @article{eells,
38   title={A setting for global analysis},
39   author={James Eells, Jr.},
40   journal={Bulletin of the American Mathematical Society},
41   volume={72},
42   number={5},
43   pages={751--807},
44   year={1966}
45 }
46 
47 @book{gorodski,
48   title   = {An introduction to Riemannian geometry},
49   author  = {Claudio Gorodski},
50   edition = {Preliminary version 3},
51   year    = {2022},
52   month   = jun,
53   url     = {https://www.ime.usp.br/~gorodski/teaching/mat5771-2022/master07-05-2022.pdf},
54 }
55