\begin{equation}
\vspace{-0.3em}
\label{eq1}
    \exp _\mathbf{z}^c(\mathbf{x})=\mathbf{x}\oplus_c(\tanh(\sqrt{c} \frac{\lambda_\mathbf{z}^c {\Vert \mathbf{x} \Vert}^2}{2} )\frac{\mathbf{x}}{\sqrt{c{\Vert \mathbf{x} \Vert_2}}} )
    \,,
\end{equation}
