differentiable_manifold.tex

{{\gamma }}_{1}\equiv {{\gamma }}_{2}\Leftrightarrow \left\{  \begin{array}{l}
{{\gamma }}_{1}(0)={{\gamma }}_{2}(0)={p},\mathrm{and\ } \\
{\left\frac{\mathrm{d}}{\mathrm{d}{t}} {\phi }\circ {{\gamma }}_{1}({t})\right\mid }_{{t}=0}={\left\frac{\mathrm{d}}{\mathrm{d}{t}} {\phi }\circ {{\gamma }}_{2}({t})\right\mid }_{{t}=0} \\
\end{array}