# Differential geometry
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- differentiable curve
- arc-length
- reparametrization of a curve
- inverse function theorem for differentiable curves
- regular differentiable curve
- arc-length reparametrization of a curve
- Frenet-serret frame
- Frenet-serret equations


- diffeomorphism
\begin{definition}
A \emph{diffeomorphism} between two differential manifolds $N$ and $M$ is a bijective function $f : N \to M$ such that both $f$ and $f^{-1}$ are continuously differentiable.
\end{definition}
- change of coordinates
- autodiffeomorphism
- examples of change of coordinatess
- Jacobian matrix
- inverse function theorem (manifolds)
- chart

- compatible pair of charts
- atlas
- compatible chart to atlas
- stereographic projection
- manifold
- n-sphere
- real projective space
- complex projective space
- Grassmanian


- tangent space