<filename>src/pug/theory/geometry/manifoldsDifferentiable/01-01-differentiable.tex<gh_stars>0

\subsection{Differentiable transition maps}

\subsubsection{Transition map recap}

Given two charts with an overlap, we have a transition mapping between the two charts of the overlap, where the mapping corresponds to a position on the manifold.

\subsubsection{Differentiable transition maps}

If this mapping is differentiable, we have a differentiable manifold.

\subsubsection{Smooth manifolds}

If transition maps are smooth (\(C^\infty \)) then the manifold is smooth.

