- Untitled
- Section vector bundles subsection basic
- Begin definition pseudobundle a emph
- Begin definition restricted pseudobundle let
- Begin definition pseudosection let mathbf
- Begin definition global and local
- Begin definition smooth vector bundle
- Begin theorem let mathbf e 1
- Begin theorem let mathbf e
- Subsection induced bundles let mathbf
- Section connections
- Begin lemma consider a vector
- Section geodesics
- Begin theorem let m g 1
- Begin lemma let m g
- Begin theorem let m g
- Begin theorem we have gamma
- Begin definition for t geq
- Begin definition we define the
- Begin theorem mathcal d is
- Begin theorem let m g 2
- Begin definition if exp p bigg
- Begin theorem let kappa x
- Begin proof most statements are
- An important identity that we
- Begin theorem nabla r t 1
- Begin theorem gauss lemma end
- Begin theorem nabla r t
- Begin theorem let m g 7
- Begin lemma let gamma a
- Begin corollary constant speed piecewise
- Begin theorem let m g 3
- Begin theorem let m g 4
- Begin theorem let m g 6
- Begin theorem let m g 5
- Next we show uniqueness end
- Begin theorem consider exponential coordinates
- Section existence of minimizing geodesics
- Begin definition complete metric space
- Begin theorem let m g 8
- Section integration on riemannian manifolds
- Add boundary term in the
- More generally we have declaremathoperator
- Begin proof what we need

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