Algorithm 5 Parallel transport of tangent vector field w from $\alpha \left(\frac{\tau }{k}\right)$ to $\alpha \left(\frac{\tau +1}{k}\right)$ denoted as $w^{\Vert }=\Pi \left(w;\alpha \left(\frac{\tau }{k}\right),\alpha \left(\frac{\tau +1}{k}\right)\right)$
1	Let lw = 〈w, w〉.
2:	$w^{\Vert }=\pi \left(w;\alpha \left(\frac{\tau -1}{k}\right),\alpha \left(\frac{\tau }{k}\right)\right)$
3:	Project w‖ into $T_{(\alpha \left(\frac{\tau }{k}\right)}(\mathcal{C})$ using Algorithm 2 and call it ${\mathit{\text{w}}}_{\mathit{\text{proj}}}^{\Vert }$.
4:	Rescale the length as $w_{\mathit{\text{proj}}}^{\Vert }=\frac{l_w{w}_{\mathit{\text{proj}}}^{\Vert }}{\langle w_{\mathit{\text{proj}}}^{\Vert },w_{\mathit{\text{proj}}}^{\Vert }\rangle }$