# 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

Improved the proof of the fact that the inclusions are continuous

Fixed the proof that the inclusions of section spaces are continuous

Added further details on the abstract isomorphism between H¹(gamma* TM) and H¹(I, R^n)

Changed the notation for the charts of the tanget bundle of H¹(I, M)

Rephrased the theorem that states that the Morse index of a geodesic is well defined

Fixed some typos, rephrased some sentences and removed unnecessary whitespace

Made it so that the TOC and the introduction section sit on the same page

Made it so that the table of contents and the references sit on their own pages

Added further explanations to the example of the staircase curve

Finished writing the introduction of the section on the structure of H¹(I, M)

Started to work on the section about the structure of H¹(I, M)

Added a reference the paper by Eells in the example about the group of units of a Banach algebra